Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44657

In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
18 Oct 2015, 13:07
2
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
Question Stats:
77% (00:47) correct 23% (00:55) wrong based on 806 sessions
HideShow timer Statistics



Manager
Joined: 11 Sep 2013
Posts: 110

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
18 Oct 2015, 13:17
1
This post was BOOKMARKED
Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png the calculated value = half of the perimeter of circle O = pi*R The length of AC = 10 => R = 5 => the calculated value = Pi * 5 Ans E



Manager
Joined: 12 Mar 2015
Posts: 100
Concentration: Leadership, Finance
GPA: 3.9
WE: Information Technology (Computer Software)

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
18 Oct 2015, 13:28
Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png IMO: 5π .Diameter is 10. So (180/360)* 2π5 = 5π



Board of Directors
Joined: 17 Jul 2014
Posts: 2743
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
18 Oct 2015, 13:45
without any calculations, we can see that AC is the diagonal of a circle. Knowing that AB=8 and AC=6 we can spot the Pythagorean triplet 345, and can deduce that AC, the diagonal is 10. Circumference of the circle must then be 10pi. Since we have only a semicircle, the length of the arc then must be 1/2*10pi = 5pi. Answer choice E.



Intern
Joined: 01 Mar 2015
Posts: 49

In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
18 Oct 2015, 22:31
Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png Triangle ABC is right angled at B, by Pythagoras theorem we have diameter of semicircle as 10 => arc ABC = π * radius = 5π Answer Choice E



Current Student
Joined: 23 Mar 2016
Posts: 34

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
02 May 2016, 14:23
I am looking for the rule that states that any angle like <B in this problem will always be right angle, can't find it in my pocket reference. Theoretical explanation from anyone? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 44657

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
03 May 2016, 01:07



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2493
Location: United States (CA)

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
03 May 2016, 05:25
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png We are given that triangle ABC is inscribed in the semicircle. Since a triangle inscribed in a semicircle is always a right triangle, triangle ABC is a right triangle. Therefore, AC is both the hypotenuse of triangle ABC and the diameter of the semicircle. We are also given that side AB = 8 and that side BC = 6. With that information, we can conclude that triangle ABC is a 6810 right triangle, in which side AC = 10. We need to determine the length of arc ABC, or, in other words, the length of half of the circumference of the circle. Since the diameter is 10, the radius is 5. We use the circumference formula C = 2∏r to obtain 10∏ as the circumference of the entire circle. The length of arc ABC is half of the circumference; therefore, its value is 5∏. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 606
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
17 May 2016, 19:23
1
This post received KUDOS
Attached is a visual that should help.
Attachments
Screen Shot 20160517 at 7.12.20 PM.png [ 151.44 KiB  Viewed 7053 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y8zh6qby Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring



Math Expert
Joined: 02 Sep 2009
Posts: 44657

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
22 Mar 2017, 13:10
Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png 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 ABC is inscribed in semicircle then ABC is a right triangle and AC=diameter=hypotenuse. Also note that the length of arc ABC is half of the circumference. \(AC=\sqrt{AB^2+BC^2}=\sqrt{64+36}=10\) > \(radius=\frac{diameter}{2}=\frac{AC}{2}=5\) > \(circumference=2\pi{r}=10\pi\) > \(arc_{ABC}=\frac{circumference}{2}=5\pi\). Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 02 Sep 2016
Posts: 750

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
08 Sep 2017, 06:20
Two methods: 1) Formula to find length of arc= Central angle/360 *2*pi*radius AC (diameter): AC^2= 8^2+6^2= 10 Putting the values in the above formula: Length= 180/360 *2*pi*5 = 5*pi 2) 345 triangle 6810 Length of arc= 2*pi*r/2= 5*pi
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.



Intern
Joined: 22 Mar 2016
Posts: 8

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
03 Mar 2018, 08:19
Can you explain how we can conclude that length of ABC is half the circle? Bunuel wrote: Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png 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 ABC is inscribed in semicircle then ABC is a right triangle and AC=diameter=hypotenuse. Also note that the length of arc ABC is half of the circumference. \(AC=\sqrt{AB^2+BC^2}=\sqrt{64+36}=10\) > \(radius=\frac{diameter}{2}=\frac{AC}{2}=5\) > \(circumference=2\pi{r}=10\pi\) > \(arc_{ABC}=\frac{circumference}{2}=5\pi\). Answer: E.



Math Expert
Joined: 02 Sep 2009
Posts: 44657

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]
Show Tags
03 Mar 2018, 08:58
AMARAAZUNWIE wrote: Can you explain how we can conclude that length of ABC is half the circle? Bunuel wrote: Bunuel wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? (A) 15π (B) 12π (C) 10π (D) 7π (E) 5π Kudos for a correct solution.Attachment: 20151019_0005.png 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 ABC is inscribed in semicircle then ABC is a right triangle and AC=diameter=hypotenuse. Also note that the length of arc ABC is half of the circumference. \(AC=\sqrt{AB^2+BC^2}=\sqrt{64+36}=10\) > \(radius=\frac{diameter}{2}=\frac{AC}{2}=5\) > \(circumference=2\pi{r}=10\pi\) > \(arc_{ABC}=\frac{circumference}{2}=5\pi\). Answer: E. Semicircle is half of the circle.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Re: In the figure shown, the triangle is inscribed in the semicircle. If
[#permalink]
03 Mar 2018, 08:58






