BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

RUSH - (exam on monday) Equal. Triangles in a Circle

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Fri Apr 03, 2009 11:57 am

RUSH - (exam on monday) Equal. Triangles in a Circle

by Kiddo25 » Fri Apr 03, 2009 12:11 pm
If an equalilateral triangle is inscribed in a circle, with perimeter of the triangle = 24. What is the approximate value for the diameter of the circle?

so all we know is each side of the equal. triangle is 8, and cutting it in half makes 30-60-90 with:
t = 4
2t = 8 (each side of the original equal. triangle)
t sq root 3 = 4 sq root 3

How can I find the diameter?
Top
Source: — Problem Solving |
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Sun Jan 04, 2009 8:09 am

by ncr_10 » Sat Apr 04, 2009 1:03 am
You must note that the radius of a circumscribed circle is 2/3 * (height of the equilateral triangle).

So in this case the radius would be (2*(4 sqrt(3))) / 3 = (8/(sqrt(3))).

The shortcut to find radius would be a/sqrt(3), where a is the length of the side of the triangle.

-ncr
Top
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Thu Aug 21, 2008 8:17 am

by cbrombe1 » Tue Apr 14, 2009 11:08 am
Can you please clarify (maybe with a picture)? Thanks!
Top
Senior | Next Rank: 100 Posts
Posts: 72
Joined: Sat Mar 28, 2009 10:05 pm
Thanked: 2 times

by nasa » Tue Apr 14, 2009 9:18 pm
If an equalilateral triangle is inscribed in a circle, with perimeter of the triangle = 24. What is the approximate value for the diameter of the circle?

Call the triangle ABC with side length "a" and the center of circle O
The hieght h = a*sqrt3/2
perimeter = 24 ==> a = 8

Look at the triange OBC making an angle 120deg at the center. (Since angle BAC is 60deg, angle BOC is 120deg) So ang OAB = (180-120)/2 = 30deg

Also, you can consider the new hight hn = h/2, due to the fact ABC is a equilateral triangle.
hn/R = sin30
==> diameter = 2R = 2*hn/sin30 = 2*h/(2*sin30) = h = 8 * 1.732 = 13.8 approx. value
Top
Post new topic Post Reply
• Page 1 of 1