Day 3: Just Enough Information

Geometry Level 3

\(ABCD\) is a cyclic quadrilateral. \(\angle ADB = \angle BDC = 45 ^ {\circ}\). Also, \(AD + DC = 50\).

Find the area of \(ABCD\).


This problem is part of the Advent Calendar 2015. This was inspired from a problem from the Kangaroo 2015!
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