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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