# Circling The Foot

Geometry Level 5

An isosceles triangle $$ABC$$ has side lengths $$CA=CB$$. $$X$$ is a point on the circumcircle of triangle $$ABC$$, lying on the arc between $$A$$ and $$B$$ not containing $$C$$, such that $$XA=100$$ and $$XB=300$$. Let $$D$$ be the foot of the perpendicular from $$C$$ to $$XB$$. What is the length of $$XD$$?

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