MathDB

Incenter-excenter geo

Source: All-Russian 2022 9.2

April 19, 2022

geometry

Problem Statement

Given is triangle

ABC

with incenter

I

and

A

-excenter

J

. Circle

\omega_b

centered at point

O_b

passes through point

B

and is tangent to line

CI

at point

I

. Circle

\omega_c

with center

O_c

passes through point

C

and touches line

BI

at point

I

. Let

O_bO_c

and

IJ

intersect at point

K

. Find the ratio

IK/KJ

.

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