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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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