MathDB

Two circles with centers

O_{1}

and

O_{2}

meet at two points

A

and

B

such that the centers of the circles are on opposite sides of the line

AB

. The lines

BO_{1}

and

BO_{2}

meet their respective circles again at

B_{1}

and

B_{2}

. Let

M

be the midpoint of

B_{1}B_{2}

. Let

M_{1}

M_{2}

be points on the circles of centers

O_{1}

and

O_{2}

respectively, such that

\angle AO_{1}M_{1}= \angle AO_{2}M_{2}

, and

B_{1}

lies on the minor arc

AM_{1}

while

B

lies on the minor arc

AM_{2}

. Show that

\angle MM_{1}B = \angle MM_{2}B

. Ciprus

Problem Statement