An isosceles triangle with one angle of 120°

[Zach.J.Dragone]

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

[Matt@VeritasPrep]

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:


Step 2:


Step 3:


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