MathDB

Let

O

be the circumcenter of the acute triangle

ABC

. Suppose points

A',B'

and

C'

are on sides

BC,CA

and

AB

such that circumcircles of triangles

AB'C',BC'A'

and

CA'B'

pass through

O

. Let

\ell_a

be the radical axis of the circle with center

B'

and radius

B'C

and circle with center

C'

and radius

C'B

. Define

\ell_b

and

\ell_c

similarly. Prove that lines

\ell_a,\ell_b

and

\ell_c

form a triangle such that it's orthocenter coincides with orthocenter of triangle

ABC

.
Proposed by Mehdi E'tesami Fard

Problem Statement