MathDB

SMT 2018 Geometry #10 2 incircles

Source:

August 8, 2023

geometry

Problem Statement

Let

ABC

be a triangle with

AB = 13

,

AC = 14

, and

BC = 15

, and let

\Gamma

be its incircle with incenter

I

. Let

D

and

E

be the points of tangency between

\Gamma

and

BC

and

AC

respectively, and let

\omega

be the circle inscribed in

CDIE

. If

Q

is the intersection point between

\Gamma

and

\omega

and

P

is the intersection point between

CQ

and

\omega

, compute the length of

P Q

.

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