MathDB

2014 preRMO p12, sum of radii of triangle incircles wanted

Source:

August 9, 2019

geometryinradiusSumright angle

Problem Statement

Let

ABCD

be a convex quadrilateral with

\angle DAB =\angle B DC = 90^o

. Let the incircles of triangles

ABD

and

BCD

touch

BD

P

and

Q

, respectively, with

P

lying in between

B

and

Q

. If

AD = 999

and

PQ = 200

then what is the sum of the radii of the incircles of triangles

ABD

and

BDC