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Synthetic Geometry

Triangles, circles, polygons, and more.

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The hypotenuse (longest side) of a right triangle with integer side lengths is 13. What is the area of the triangle?

\(ABCD\) is a square with side length 10, and \(P\) lies on \(AB\). What is the area of triangle \(PCD\)?

\(\triangle ABC\) has \(D,E\) on \(AB, AC\) respectively so that \(DE\) and \(BC\) are parallel. If \(AD = 3\), \(DB = 6\), and \(DE = 5\), what is \(BC\)?

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