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2015 AMC 10B Problems/Problem 19

Revision as of 12:03, 5 March 2015 by Hesa57 (talk | contribs) (Created page with "==Problem== In <math>\triangle{ABC}</math>, <math>\angle{C} = 90^{\circ}</math> and <math>AB = 12</math>. Squares <math>ABXY</math> and <math>ACWZ</math> are constructed outsi...")
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Problem

In $\triangle{ABC}$, $\angle{C} = 90^{\circ}$ and $AB = 12$. Squares $ABXY$ and $ACWZ$ are constructed outside of the triangle. The points $X, Y, Z$, and $W$ lie on a circle. What is the perimeter of the triangle?

$\textbf{(A) }12+9\sqrt{3}\qquad\textbf{(B) }18+6\sqrt{3}\qquad\textbf{(C) }12+12\sqrt{2}\qquad\textbf{(D) }30\qquad\textbf{(E) }32$

Solution

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