May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 18 Aug 2011
Posts: 47

In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
Updated on: 26 Aug 2011, 01:59
Question Stats:
64% (01:39) correct 36% (01:46) wrong based on 452 sessions
HideShow timer Statistics
In the diagram above, if arc ABC is a semicircle, what is the length of AC? (1) AD = 2.5 (2) DC = 10 Attachment:
cricle.jpg [ 23.94 KiB  Viewed 33446 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Berbatov on 26 Aug 2011, 01:24.
Last edited by Berbatov on 26 Aug 2011, 01:59, edited 1 time in total.




Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
14 Jan 2012, 17:27
karthiksms wrote: I'm not able to understand the ans to this q.. could someone elaborate please? Attachment:
12.JPG [ 15.74 KiB  Viewed 35539 times ]
In the diagram above, if arc ABC is a semicircle, what is the length of AC?You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.So, as given that AC is a diameter then angle ABC is a right angle. • Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. Thus, the perpendicular BD divides right triangle ABC into two similar triangles ADB and BDC (which are also similar to big triangle ABC). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: AB/AC=AD/AB=BD/BC. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from AB, AD, AC, BC, BD, CD then we'll be able to find the other 4. We are given that BD=5 thus to find AC we need to know the length of any other line segment. Also in such kind of triangles might be useful to equate the areas to find the length of some line segment, for example area of ABC=1/2*AC*BD=1/2*AB*BC (for more check: triangles106177.html, geometryproblem106009.html, mgmatdshelp94037.html, help108776.html) (1) AD = 2.5. Sufficient. (2) DC = 10. Sufficient. Answer: D. Hope it helps.
_________________




Senior Manager
Joined: 03 Mar 2010
Posts: 372

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
26 Aug 2011, 02:41
Stmt1: AD=2.5 In triangle ABD, tan <bad = 5/2.5=2 Hence we know the value of <bad Also, AB^2=AD^2+BD^2 =2.5^2+5^2= 31.25 AB =\(\sqrt{31.25}\) In triangle ABC, <ABC is right angle. We know one side (AB) and one angel (<bad) in triangle ABC. Sufficient to find AC. Stmt2: By similar reason, in triangle BDC we can find out <bcd Also, BC^2=5^2+10^=125 BC = \(\sqrt{125}\) In triangle ABC we know one side (BC) and one angel (<bcd). Sufficient to find AC. OA D.
_________________
My dad once said to me: Son, nothing succeeds like success.



Manager
Joined: 28 Jul 2011
Posts: 88

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
03 Nov 2011, 10:45
D. It can be visualized if you split the triangle into 2; then notice you have a proportion with 3 numbers missing 1.



Intern
Joined: 07 Oct 2011
Posts: 27

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
14 Jan 2012, 16:37
I'm not able to understand the ans to this q.. could someone elaborate please?



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
22 May 2013, 03:40
Bumping for review and further discussion.
_________________



Manager
Joined: 15 Aug 2013
Posts: 243

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
24 May 2014, 14:16
Bunuel wrote: Thus, the perpendicular BD divides right triangle ABC into two similar triangles ADB and BDC (which are also similar to big triangle ABC). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: AB/AC=AD/AB=BD/BC. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from AB, AD, AC, BC, BD, CD then we'll be able to find the other 4.We are given that BD=5 thus to find AC we need to know the length of any other line segment.
Hope it helps.
Hi Bunuel, I have a theoretical question based on the highlighted statement above: It seems as though there is always overlap of sides(since we have similar triangles) so your highlighted statement looks to be true. For the sake of saving time  i was trying to get a deeper understanding of this method  Can there ever be a case when they give us the length of two sides, but since they are ONLY of one triangle, we can't make the leap onto others(minus the obvious correlations between the ratio) Meaning, In this same problem, if Statement 1 and 2 were given but if we weren't given a value of BD, then we wouldn't have been able to solve it. Correct? Is it safe to say that two sides will ALWAYS create sufficiency, even if the two sides are on the same triangle?



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
24 May 2014, 14:29
russ9 wrote: Bunuel wrote: Thus, the perpendicular BD divides right triangle ABC into two similar triangles ADB and BDC (which are also similar to big triangle ABC). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: AB/AC=AD/AB=BD/BC. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from AB, AD, AC, BC, BD, CD then we'll be able to find the other 4.We are given that BD=5 thus to find AC we need to know the length of any other line segment.
Hope it helps.
Hi Bunuel, I have a theoretical question based on the highlighted statement above: It seems as though there is always overlap of sides(since we have similar triangles) so your highlighted statement looks to be true. For the sake of saving time  i was trying to get a deeper understanding of this method  Can there ever be a case when they give us the length of two sides, but since they are ONLY of one triangle, we can't make the leap onto others(minus the obvious correlations between the ratio) Meaning, In this same problem, if Statement 1 and 2 were given but if we weren't given a value of BD, then we wouldn't have been able to solve it. Correct? Is it safe to say that two sides will ALWAYS create sufficiency, even if the two sides are on the same triangle? If we were not give the length of BD, then the answer would be C: 2.5/BD = BD/10 > BD = 5 > we can find AC.
_________________



Current Student
Joined: 28 Sep 2013
Posts: 66
Location: United States (NC)
Concentration: Operations, Technology
WE: Information Technology (Consulting)

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
17 Jun 2014, 20:09
Bunuel wrote: karthiksms wrote: I'm not able to understand the ans to this q.. could someone elaborate please? Attachment: 12.JPG In the diagram above, if arc ABC is a semicircle, what is the length of AC?You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.So, as given that AC is a diameter then angle ABC is a right angle. • Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. Thus, the perpendicular BD divides right triangle ABC into two similar triangles ADB and BDC (which are also similar to big triangle ABC). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: AB/AC=AD/AB=BD/BC. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from AB, AD, AC, BC, BD, CD then we'll be able to find the other 4. We are given that BD=5 thus to find AC we need to know the length of any other line segment. Also in such kind of triangles might be useful to equate the areas to find the length of some line segment, for example area of ABC=1/2*AC*BD=1/2*AB*BC (for more check: triangles106177.html, geometryproblem106009.html, mgmatdshelp94037.html, help108776.html) (1) AD = 2.5. Sufficient. (2) DC = 10. Sufficient. Answer: D. Hope it helps. Hi Bunuel, AB/AC=AD/AB=BD/BC means that AB and AC are corresponding , and also AD and AB are corresponding and BD and BC are coresponding angles. Please tell which angles are they opposite to, because AB is opposite to angle BCA, and AC is opposite to angle ABC. How are these two angles corresponding. Same doubt for other corresponding angles also. Please clarify.
_________________
_________________________________ Consider Kudos if helpful



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
18 Jun 2014, 01:58
thoufique wrote: Bunuel wrote: In the diagram above, if arc ABC is a semicircle, what is the length of AC?You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.So, as given that AC is a diameter then angle ABC is a right angle. • Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. Thus, the perpendicular BD divides right triangle ABC into two similar triangles ADB and BDC (which are also similar to big triangle ABC). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: AB/AC=AD/AB=BD/BC. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from AB, AD, AC, BC, BD, CD then we'll be able to find the other 4. We are given that BD=5 thus to find AC we need to know the length of any other line segment. Also in such kind of triangles might be useful to equate the areas to find the length of some line segment, for example area of ABC=1/2*AC*BD=1/2*AB*BC (for more check: triangles106177.html, geometryproblem106009.html, mgmatdshelp94037.html, help108776.html) (1) AD = 2.5. Sufficient. (2) DC = 10. Sufficient. Answer: D. Hope it helps. Hi Bunuel, AB/AC=AD/AB=BD/BC means that AB and AC are corresponding , and also AD and AB are corresponding and BD and BC are coresponding angles. Please tell which angles are they opposite to, because AB is opposite to angle BCA, and AC is opposite to angle ABC. How are these two angles corresponding. Same doubt for other corresponding angles also. Please clarify. In similar triangles corresponding sides are the sides opposite the same angles. In triangle ABC: AB is opposite blue angle, AC is opposite right angle. In triangle ADB: AD is opposite blue angle, AB is opposite right angle. In triangle BDC: BD is opposite blue angle, BC is opposite right angle. Since the above three triangles are similar then the ratio of these sides must be the same. Hope it's clear.
_________________



Current Student
Joined: 28 Sep 2013
Posts: 66
Location: United States (NC)
Concentration: Operations, Technology
WE: Information Technology (Consulting)

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
18 Jun 2014, 07:06
Thanks a lot bunuel , its clear now. Can the ratios be taken using red angles also. In that case we get BC/AC = BD/AB = CD/BC. If yes, then depending upon the unknown, we can consider appropriate corresponding angles.
_________________
_________________________________ Consider Kudos if helpful



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
18 Jun 2014, 08:40
thoufique wrote: Thanks a lot bunuel , its clear now. Can the ratios be taken using red angles also. In that case we get BC/AC = BD/AB = CD/BC. If yes, then depending upon the unknown, we can consider appropriate corresponding angles. BC/AC = BD/AB = CD/BC is correct. And yes, you can equate ratios of any pair of corresponding angles.
_________________



Current Student
Joined: 28 Sep 2013
Posts: 66
Location: United States (NC)
Concentration: Operations, Technology
WE: Information Technology (Consulting)

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
18 Jun 2014, 09:57
Bunuel wrote: thoufique wrote: Thanks a lot bunuel , its clear now. Can the ratios be taken using red angles also. In that case we get BC/AC = BD/AB = CD/BC. If yes, then depending upon the unknown, we can consider appropriate corresponding angles. BC/AC = BD/AB = CD/BC is correct. And yes, you can equate ratios of any pair of corresponding angles. Thanks a ton bunuel, was struggling with this for a long time.
_________________
_________________________________ Consider Kudos if helpful



Intern
Joined: 18 May 2016
Posts: 35

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
14 Jun 2016, 02:20
Bunuel wrote: thoufique wrote: Bunuel wrote: [/img] In the diagram above, if arc ABC is a semicircle, what is the length of AC?
You should know the following properties to solve this question: • A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.
So, as given that AC is a diameter then angle ABC is a right angle.
• Perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle.
Thus, the perpendicular BD divides right triangle ABC into two similar triangles ADB and BDC (which are also similar to big triangle ABC). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles). For example: AB/AC=AD/AB=BD/BC. This property (sometimes along with Pythagoras) will give us the following: if we know ANY 2 values from AB, AD, AC, BC, BD, CD then we'll be able to find the other 4. We are given that BD=5 thus to find AC we need to know the length of any other line segment.
Also in such kind of triangles might be useful to equate the areas to find the length of some line segment, for example area of ABC=1/2*AC*BD=1/2*AB*BC \
(1) AD = 2.5. Sufficient. (2) DC = 10. Sufficient.
Answer: D.
Hope it helps. Hi Bunuel, AB/AC=AD/AB=BD/BC means that AB and AC are corresponding , and also AD and AB are corresponding and BD and BC are coresponding angles. Please tell which angles are they opposite to, because AB is opposite to angle BCA, and AC is opposite to angle ABC. How are these two angles corresponding. Same doubt for other corresponding angles also. Please clarify. In similar triangles corresponding sides are the sides opposite the same angles.
In triangle ABC: AB is opposite blue angle, AC is opposite right angle. In triangle ADB: AD is opposite blue angle, AB is opposite right angle.In triangle BDC: BD is opposite blue angle, BC is opposite right angle. Since the above three triangles are similar then the ratio of these sides must be the same. Hope it's clear. Bunuel, I understand this . However i don't understand this. How can you know AD is opposite blue and not red angle? Thanks,



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
14 Jun 2016, 02:26
plalud wrote: Bunuel, I understand this . However i don't understand this. How can you know AD is opposite blue and not red angle?
Thanks, Please make a post so that it's clear what you are asking, quoting an image etc. We k ow which angles are equal to each other, blue = blue and red = red. Corresponding sides are opposite equal angles.
_________________



Intern
Joined: 18 May 2016
Posts: 35

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
14 Jun 2016, 03:23
Bunuel I cannot insert any U r l. My question is: In ABC we have a right, a blue and a red angle. In ADB, we have a right, a blue and a red angle. The corresponding right one is obviously the right one. But how can we know which angle in ADB corresponds to the blue angle in ABC? I hope i am clear.



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
14 Jun 2016, 07:07
plalud wrote: Bunuel I cannot insert any U r l. My question is: In ABC we have a right, a blue and a red angle. In ADB, we have a right, a blue and a red angle. The corresponding right one is obviously the right one. But how can we know which angle in ADB corresponds to the blue angle in ABC? I hope i am clear. \(\angle BAC + \angle ACB = 90°\); \(\angle BAC + \angle ABD = 90°\); Thus \(\angle ACB=\angle ABD\). Similarly: \(\angle BAC + \angle ACB = 90°\); \(\angle CBD + \angle ACB = 90°\); Thus \(\angle BAC =\angle CBD\).
_________________



Board of Directors
Joined: 17 Jul 2014
Posts: 2552
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
25 Jul 2017, 06:55
I got to the right answer just by knowing the properties of the inscribed triangle... ABC is a right triangle 306090 we know BD finding AD or BC can help us find the legs and hypotenuse of the big triangle...
1. gives us AD, thus we can find AB, and from here, apply 306090 triangle properties to find AC. 2. gives us DC, from here, we can find BC, and again apply 306090 triangle properties to find AC.
the answer is D.



NonHuman User
Joined: 09 Sep 2013
Posts: 11007

Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
Show Tags
13 Sep 2018, 11:42
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: In the diagram above, if arc ABC is a semicircle, what is
[#permalink]
13 Sep 2018, 11:42






