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Question about inscribed equilateral triangle

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by gmattesttaker2 » Sun Nov 24, 2013 2:17 pm
Hello,

Can you please assist with this:

An equilateral triangle of side 12 is inscribed in a circle, what is the area of
the circle?


OA: C


My approach was as shown in this attachment. One thing I wanted to know was can the base of the triangle i.e. can BC be the diameter of the circle?

From the diagram, I am getting height h of triangle ABC to be 6.

To calculate r I am assuming that OC splits angle ACB (which is 60 degrees) into 2 equal halves of 30 degrees each. I was wondering if this assumption is correct? Can it happen that OC splits angle ACB into 2 halves of 40 degrees and 20 degrees each?

Thanks for your help,
Sri


O
Attachments
Inscribed triangle.png
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Source: — Problem Solving |

by [email protected] » Sun Nov 24, 2013 5:50 pm
Hi Sri,

Your math work is correct. I don't see any answers to choose from, but your diagram and breakdown of the equilateral triangle are correct.

In answer to your questions:

1) An equilateral triangle inscribed in a circle CANNOT have any of its sides equal to the diameter of the circle.
2) Breaking down the equilateral triangle into equal thirds will always yield three 30/30/120 triangles. These triangles can be further broken down into two equal 30/60/90 right triangles. There is no other option that creates equal-sized sub-triangles.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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