MathDB

Incenter, excenter problem show that two circles are tangent

Source: IMOC 2021 G9

August 11, 2021

geometrytangent circlesincenterexcenterreflection

Problem Statement

Let the incenter and the

A

-excenter of

\triangle ABC

I

and

I_A

, respectively. Let

BI

intersect

AC

E

and

CI

intersect

AB

F

. Suppose that the reflections of

I

with respect to

EF

FI_A

EI_A

are

X

Y

Z

, respectively. Show that

\odot(XYZ)

and

\odot(ABC)

are tangent to each other.