MathDB

A circle having common centre with the circumcircle of triangle

ABC

meets the sides of the triangle at six points forming convex hexagon

A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}

(

A_{1}

and

A_{2}

lie on

BC

B_{1}

and

B_{2}

lie on

AC

C_{1}

and

C_{2}

lie on

AB

). If

A_{1}B_{1}

is parallel to the bisector of angle

B

, prove that

A_{2}C_{2}

is parallel to the bisector of angle

C

.
Proposed by S. Berlov

Problem Statement