Let \(X\) be a point outside a circle, and let \(A\) and \(C\) be points on the circle such that \(\overline{XA}\) and \(\overline{XC}\) are tangent to the circle. Points \(B\) and \(D\) are on the circle such that \(B, D,\) and \(X\) are collinear. Prove that \(AB \cdot CD = BC \cdot DA\).
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