GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Jan 2020, 12:20

### 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

# Given the circle to the right, with center O, diameter AOB, a radius

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60460
Given the circle to the right, with center O, diameter AOB, a radius  [#permalink]

### Show Tags

23 Mar 2016, 12:47
00:00

Difficulty:

5% (low)

Question Stats:

91% (00:43) correct 9% (01:30) wrong based on 79 sessions

### HideShow timer Statistics

Given the circle to the right, with center O, diameter AOB, a radius of 5, and the inscribed triangle ABC, what is the length of AC?

A. 4.5
B. 5
C. 6
D. 6.5
E. 7

Attachment:

circletrianglequestion.gif [ 5.04 KiB | Viewed 2466 times ]

_________________
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: Given the circle to the right, with center O, diameter AOB, a radius  [#permalink]

### Show Tags

23 Mar 2016, 20:38
ACB is a right angle triangle.
AB = 10 is the hypotenuse
BC = 8
AC = $$\sqrt{10^2 - 8^2}$$ = 6

Current Student
Joined: 12 Aug 2015
Posts: 2550
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: Given the circle to the right, with center O, diameter AOB, a radius  [#permalink]

### Show Tags

04 Apr 2016, 15:16
Angle within a semicircle is always 90 => the triangle is a right triangle => AC = √(100-64) => 6 i.e.C is correct
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15929
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Given the circle to the right, with center O, diameter AOB, a radius  [#permalink]

### Show Tags

01 Dec 2019, 15:51
Hi All,

We're told that in the circle with center O, AOB is the diameter, the radius of the circle is 5 and triangle ABC is inscribed. We're asked for the the length of AC. This question is based on some specific Geometry patterns - and if you recognize them, then you can answer this question without doing much math at all.

To start, any triangle in a circle that has all 3 vertices ON the circumference AND has one side that is the diameter of the circle is a RIGHT TRIANGLE. Thus, Angle C is a 90-degree angle.

Next, since the radius of the circle is 5, the diameter is 10. We now know two of the sides of the right triangle (8 and 10 - which is the hypotenuse). You can use the Pythagorean Theorem (A^2 + B^2 = C^2) to find the missing side OR you might recognize that we're dealing with a 3/4/5 right triangle that has been 'doubled' (into a 6/8/10 right triangle). Thus, the missing side is 6.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: Given the circle to the right, with center O, diameter AOB, a radius   [#permalink] 01 Dec 2019, 15:51
Display posts from previous: Sort by