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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An isosceles triangle with one angle of 120°
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Zach.J.Dragone
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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
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
