You do this in two ways.
First method:
arc ABC =24
The triangle is an equilateral triangle the angle b would be 60, therefore the central angle formed at the center of the circle is 120. You can easily find the arc AC => (120/360)*2(pi)r
arc AC+ arc ABC = 2(pi)r
(120/360)*2(pi)r + 24 = 2(pi)r
pi=22/7
If you solve the above equation, r= 5.7
diameter = 2*5.7 = 11.4= 11 approx.
Second Method (easier one):
The triangle is an equilateral triangle therefore every arc would be of same length.
arc AB = 12,
arc BC = 12
arc AC = 12
arc AB+arc BC+arc AC = 36
36=2(pi)r
r=5.7
d=2r=11.4 or 11
Let me know if you still have any doubts.
circles
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Source: Beat The GMAT — Problem Solving |
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parallel_chase
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pepeprepa
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The equilateral triangle is inscribed in the circle, so there are 3 arcs between the vertex of the triangle: AB, BC, AC. Given the triangle is equilateral they will have the same length.
You know 24=2/3X X=36
And each one is 12
You know 24=2/3X X=36
And each one is 12
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pbanavara
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The first method is awesome - agreed a little time consuming .. but gets down to the basics .. I just got the first part that is angle subtended at the center .. and then gave up - because of lack of time.
Thanks for the explanation.
Thanks for the explanation.
