MathDB

12

Part of 2014 India PRMO

Problems(1)

2014 preRMO p12, sum of radii of triangle incircles wanted

Source:

8/9/2019
Let ABCDABCD be a convex quadrilateral with ∠DAB=∠BDC=90o\angle DAB =\angle B DC = 90^o. Let the incircles of triangles ABDABD and BCDBCD touch BDBD at PP and QQ, respectively, with PP lying in between BB and QQ. If AD=999AD = 999 and PQ=200PQ = 200 then what is the sum of the radii of the incircles of triangles ABDABD and BDCBDC ?
geometryinradiusSumright angle