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2017 AMC 10A Problem 22

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2017 AMC 10A Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

Circles · difficulty 4 of 5 · about 8 min · position P21-25

Sides $\overline{AB}$ and $\overline{AC}$ of equilateral triangle $ABC$ are tangent to a circle at points $B$ and $C$ respectively. What fraction of the area of $\triangle ABC$ lies outside the circle?

A)
$\frac{4\sqrt{3}\pi}{27}-\frac{1}{3}$
B)
$\frac{\sqrt{3}}{2}-\frac{\pi}{8}$
C)
$\frac{1}{2}$
D)
$\sqrt{3}-\frac{2\sqrt{3}\pi}{9}$
E)
$\frac{4}{3}-\frac{4\sqrt{3}\pi}{27}$

2017 AMC 10A Problem 22

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