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Find $r_1+r_2$

Source: Moldova TST 1998

August 8, 2023

geometry

Problem Statement

Two triangles

ABC

and

BDE

have vertexes

C

and

E

on the same side of the line

AB{}

and

AB=a<BD

. Denote

\{P\}=CE\cap AB

and

\gamma=m(\angle CPA)

. Let

r_1

be the radius of the inscribed cricle of triangle

PAC

and

r_2

the radius of the excircle of triangle

PDE

, tangent to the side

DE

. Find

r_1+r_2

.

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