Problem

TxO Math Bowl 2024 - Team Contest - Problem 10

Let $\triangle ABC$ have side lengths $10$ , $17$ , and $21$ . Suppose that square $ABX_1X_2$ is constructed such that $X_1$ and $C$ lie on the opposite side of $\overleftrightarrow{AB}$ . Construct $BCY_1Y_2$ , and $CAZ_1Z_2$ similarly.

Denote the pairwise intersections of $\overleftrightarrow{X_1X_2}$ , $\overleftrightarrow{Y_1Y_2}$ , $\overleftrightarrow{Z_1Z_2}$ as $J, K, L$ , and denote pairwise intersections of $\overleftrightarrow{X_1Y_2}$ , $\overleftrightarrow{Y_1Z_2}$ , $\overleftrightarrow{Z_1X_2}$ as $P, Q, R$ .

Find the shared area between triangles $JKL$ and $PQR$ .

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Problem Tags: 2-d Geometry

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Category: TxO Math Bowl Team Contest
Points: 4
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