Given that \(\overline{AP} \cong \overline{XB},\) prove that \(\overline{AB} \cong \overline{XP}.\) After you've attempted a proof, watch the video below for a solution.

We have two overlapping congruent circles. Their intersection points are \(A\) and \(B.\) Point \(C\) is on the circumference of the first circle, while \(D\) is on the second. Given that \(\overline{AD} \cong \overline{AC},\) prove that \(\angle ADB = \angle BCA.\)