MathDB

Triangular tangents

Source: 2017 AMC10 #22

February 8, 2017

AMCAMC 10geometry2017 AMC 10A

Problem Statement

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?

<span class='latex-bold'>(A) </span>\dfrac{4\sqrt{3}\pi}{27}-\frac{1}{3}\qquad <span class='latex-bold'>(B) </span> \frac{\sqrt{3}}{2}-\frac{\pi}{8}\qquad <span class='latex-bold'>(C) </span> \frac{1}{2} \qquad <span class='latex-bold'>(D) </span>\sqrt{3}-\frac{2\sqrt{3}\pi}{9}\qquad <span class='latex-bold'>(E) </span> \frac{4}{3}-\dfrac{4\sqrt{3}\pi}{27}

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