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An isosceles triangle with one angle of 120°

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by Zach.J.Dragone » Thu Dec 12, 2013 8:10 am
An isosceles triangle with one angle of 120° is inscribed in a circle of radius 2. This triangle is rotated 90° about the center of the circle. What is the total area covered by the triangle throughout this movement, from starting point to final resting point?

A. (4pi)/3

B. (8pi)/3

C. 4pi

D. (4pi)/3 - √3

E. (25pi)/12 -√3

Spoiler: E
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by Matt@VeritasPrep » Thu Dec 12, 2013 5:13 pm
This is NOT a question that would appear on the GMAT - it requires a few too many steps, and the only shortcut I see that would allow you to reasonably solve it in two minutes requires an understanding of Mamikon's Visual Calculus, specifically the area of a tangent sweep.

That said, here's a way to do it using GMAT-approved geometry (though it took me like 10 minutes)! Hope you enjoy it, it was fun to solve.

Step 1:
Image

Step 2:
Image

Step 3:
Image

PS the "thanks" tip jar is definitely open for this one, it took a while :D
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