A geometry problem by abhishek anandGeometry 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?