A geometry problem by abhishek anand

Geometry Level 4

. Let ABCD be a convex quadrilateral with 6 DAB = 6 BDC = 90◦ . Let the incircles of triangles ABD and BCD touch BD at P and Q, respectively, with P lying in between B and Q. If AD = 999 and P Q = 200 then what is the sum of the radii of the incircles of triangles ABD and BDC?

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