It is currently 17 Oct 2017, 11:55

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the figure shown, the triangle is inscribed in the semicircle. If

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128577 [1], given: 12180

In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]

### Show Tags

18 Oct 2015, 13:07
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

72% (00:49) correct 28% (00:57) wrong based on 703 sessions

### HideShow timer Statistics

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.

[Reveal] Spoiler:
Attachment:

2015-10-19_0005.png [ 4.5 KiB | Viewed 6235 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128577 [1], given: 12180

Manager
Joined: 11 Sep 2013
Posts: 112

Kudos [?]: 87 [0], given: 26

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.

[Reveal] Spoiler:
Attachment:
2015-10-19_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

Kudos [?]: 87 [0], given: 26

Manager
Joined: 12 Mar 2015
Posts: 103

Kudos [?]: 26 [0], given: 92

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.

[Reveal] Spoiler:
Attachment:
2015-10-19_0005.png

IMO: 5π .Diameter is 10. So (180/360)* 2π5 = 5π

Kudos [?]: 26 [0], given: 92

CEO
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 392 [0], given: 182

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
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 3-4-5, 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.

Kudos [?]: 392 [0], given: 182

Manager
Joined: 01 Mar 2015
Posts: 50

Kudos [?]: 75 [0], given: 6

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.

[Reveal] Spoiler:
Attachment:
2015-10-19_0005.png

Triangle ABC is right angled at B,
by Pythagoras theorem we have diameter of semicircle as 10

=> arc ABC = π * radius = 5π

Kudos [?]: 75 [0], given: 6

Current Student
Joined: 23 Mar 2016
Posts: 37

Kudos [?]: 5 [0], given: 0

Schools: Tulane '18 (M)
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

Kudos [?]: 5 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128577 [0], given: 12180

Re: In the figure shown, the triangle is inscribed in the semicircle. If [#permalink]

### Show Tags

03 May 2016, 01:07
Expert's post
1
This post was
BOOKMARKED
glt13 wrote:
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

A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).

The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled (right angel being the angle opposite the diameter/hypotenuse).
_________________

Kudos [?]: 128577 [0], given: 12180

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1630

Kudos [?]: 836 [2], given: 2

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
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.

[Reveal] Spoiler:
Attachment:
2015-10-19_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 6-8-10 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∏.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 836 [2], given: 2

Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 404

Kudos [?]: 474 [0], given: 53

Location: United States (CA)
Age: 37
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
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-17 at 7.12.20 PM.png [ 151.44 KiB | Viewed 4650 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

Kudos [?]: 474 [0], given: 53

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128577 [0], given: 12180

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.

[Reveal] Spoiler:
Attachment:
2015-10-19_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.

$$AC=\sqrt{AB^2+BC^2}=\sqrt{64+36}=10$$ --> $$radius=\frac{diameter}{2}=\frac{AC}{2}=5$$ --> $$circumference=2\pi{r}=10\pi$$ --> $$arc_{ABC}=\frac{circumference}{2}=5\pi$$.

_________________

Kudos [?]: 128577 [0], given: 12180

Director
Joined: 02 Sep 2016
Posts: 778

Kudos [?]: 41 [0], given: 267

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) 3-4-5 triangle
6-8-10

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.

Kudos [?]: 41 [0], given: 267

Re: In the figure shown, the triangle is inscribed in the semicircle. If   [#permalink] 08 Sep 2017, 06:20
Display posts from previous: Sort by