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Math Prize 2016 Problem 19

Source:

September 12, 2016
Math Prize for Girls

Problem Statement

In the coordinate plane, consider points A=(0,0)A = (0, 0), B=(11,0)B = (11, 0), and C=(18,0)C = (18, 0). Line ℓA\ell_A has slope 1 and passes through AA. Line ℓB\ell_B is vertical and passes through BB. Line ℓC\ell_C has slope −1-1 and passes through CC. The three lines ℓA\ell_A, ℓB\ell_B, and ℓC\ell_C begin rotating clockwise about points AA, BB, and CC, respectively. They rotate at the same angular rate. At any given time, the three lines form a triangle. Determine the largest possible area of such a triangle.
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