# Difference between revisions of "2019 AMC 12B Problems/Problem 12"

## Problem

Right triangle $ACD$ with right angle at $C$ is constructed outward on the hypotenuse $AC$ of isosceles right triangle $ABC$ with leg length 1, as shown, so that the two triangles have equal perimeters. What is sin(2 BAD)?

Would you please fix the Latex above? Thanks.

$\textbf{(A) } \frac{1}{3} \qquad\textbf{(B) } \frac{\sqrt{2}}{2} \qquad\textbf{(C) } \frac{3}{4} \qquad\textbf{(D) } \frac{7}{9} \qquad\textbf{(E) } \frac{\sqrt{3}}{2}$

## Solution

D 7/9 (SuperWill)