# Circle Tangent Lengths

Geometry Level 5

Given circle $$\Gamma$$, point $$A$$ is chosen outside of $$\Gamma$$. Tangents $$AB$$ and $$AC$$ to $$\Gamma$$ are drawn, such that $$B$$ and $$C$$ lie on the circumference of $$\Gamma$$. $$K$$ is a point on the circumference of $$\Gamma$$ contained within $$ABC$$. Let $$D, E$$ and $$F$$ be the foot of the perpendiculars from $$K$$ to $$BC, AC$$ and $$AB$$, respectively. If $$KF = 20$$ and $$KE = 28$$, what is $$KD^2$$?

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