Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

I'm not able to understand the ans to this q.. could someone elaborate please?

Attachment:

12.JPG [ 15.74 KiB | Viewed 10862 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.

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?

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. _________________

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.

(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

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.

(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.

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

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 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

Re: In the diagram above, if arc ABC is a semicircle, what is [#permalink]

Show Tags

27 Jun 2015, 13:08

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]

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?

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?

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?

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

Time is a weird concept. It can stretch for seemingly forever (like when you are watching the “Time to destination” clock mid-flight) and it can compress and...