MathDB
2006 AMC 10 #16

Source:

August 20, 2011
geometryPythagorean Theorem

Problem Statement

A circle of radius 1 is tangent to a circle of radius 2. The sides of ABC \triangle ABC are tangent to the circles as shown, and the sides AB \overline{AB} and AC \overline{AC} are congruent. What is the area of ABC \triangle ABC?
[asy]defaultpen(black+linewidth(0.7)); size(7cm); real t=2^0.5; D((0,0)--(4*t,0)--(2*t,8)--cycle, black); D(CR((2*t,2),2), black); D(CR((2*t,5),1), black); dot(origin^^(4t,0)^^(2t,8)); label("B", (0,0), SW); label("C", (4*t,0), SE); label("A", (2*t,8), N); D((2*t,2)--(2*t,4), black); D((2*t,5)--(2*t,6), black); MP('2', (2*t,3), W); MP('1',(2*t, 5.5), W);[/asy]
<spanclass=latexbold>(A)</span>352<spanclass=latexbold>(B)</span>152<spanclass=latexbold>(C)</span>643<spanclass=latexbold>(D)</span>162<spanclass=latexbold>(E)</span>24 <span class='latex-bold'>(A) </span> \frac {35}2 \qquad <span class='latex-bold'>(B) </span> 15\sqrt {2} \qquad <span class='latex-bold'>(C) </span> \frac {64}3 \qquad <span class='latex-bold'>(D) </span> 16\sqrt {2} \qquad <span class='latex-bold'>(E) </span> 24