MathDB

Let

O

be the circumcircle of a

\Delta ABC

and let

I

be its incenter, for a point

P

of the plane let

f(P)

be the point obtained by reflecting

P'

by the midpoint of

OI

, with

P'

the homothety of

P

with center

O

and ratio

\frac{R}{r}

with

r

the inradii and

R

the circumradii,(understand it by \frac{OP}{OP'}\equal{}\frac{R}{r}). Let

A_1

B_1

and

C_1

the midpoints of

BC

AC

and

AB

, respectively. Show that the rays

A_1f(A)

B_1f(B)

and

C_1f(C)

concur on the incircle.

Problem Statement