G9

Part of 2021-IMOC

Problems(1)

Incenter, excenter problem show that two circles are tangent

Source: IMOC 2021 G9

Let the incenter and the

A

\triangle ABC

I

I_A

, respectively. Let

BI

AC

E

CI

AB

F

. Suppose that the reflections of

I

with respect to

EF

FI_A

EI_A

X

Y

Z

, respectively. Show that

\odot(XYZ)

\odot(ABC)

are tangent to each other.

geometrytangent circlesincenterexcenterreflection