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AMC 12 Mock Exam 5 Problem 4

Problem 4 of 25

A rectangle with side lengths 66 and 88 is inscribed in a circle. What is the area of the region that is inside the circle but outside the rectangle?

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Solution

The rectangle's diagonal, 62+82=10\sqrt{6^2+8^2}=10, is a diameter (an inscribed right angle subtends a diameter), so the radius is 55. The requested area is 25π−6⋅8=25π−4825\pi-6\cdot8=\boxed{25\pi-48}.

Tagged: rectangle inscribed in a circle