# The purple point

Geometry Level 4

$$\triangle ABC$$ is an isosceles triangle with $$AB=AC=25$$ and $$BC=14$$. $$AD$$ is a height from $$A$$ in $$\triangle ABC$$, $$E$$ is the midpoint of $$AD$$ and $$DF$$ is a height from $$D$$ in $$\triangle EDC$$.

If $$\dfrac{AF}{BF}=\dfrac{a}{b}$$ for coprime positive integers $$a$$ and $$b$$, find $$a+b$$.

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