Day 3: Just Enough Information

Geometry Level 3

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

Find the area of ABCDABCD.


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