# Bisectors

Geometry Level 4

Let $$ABCD$$ be a trapezoid with $$AB//CD$$. The bisectors of $$\angle CDA$$ and $$\angle DAB$$ meet at $$E$$, the bisectors of $$\angle ABC$$ and $$\angle BCD$$ meet at $$F$$, the bisectors of $$\angle BCD$$ and $$\angle CDA$$ meet at G, and the bisectors of $$\angle DAB$$ and $$\angle ABC$$ meet at $$H$$. Quadrilaterals $$EABF$$ and $$EDCF$$ have areas $$24$$ and $$36$$, respectively, and triangle $$ABH$$ has area $$25$$.

The area of triangle $$CDG$$ can be expressed as $$\dfrac{m}{n}$$, where $$m,n$$ are coprime positive integers.

Find $$m+n$$.

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