MathDB

Let

ABC

be a triangle and let

I

and

O

denote its incentre and circumcentre respectively. Let

\omega_A

be the circle through

B

and

C

which is tangent to the incircle of the triangle

ABC

; the circles

\omega_B

and

\omega_C

are defined similarly. The circles

\omega_B

and

\omega_C

meet at a point

A'

distinct from

A

; the points

B'

and

C'

are defined similarly. Prove that the lines

AA',BB'

and

CC'

are concurrent at a point on the line

IO

.
(Russia) Fedor Ivlev

Problem Statement