MathDB

Circles

{\omega_1}

{\omega_2}

are externally tangent at point M and tangent internally with circle

{\omega_3}

at points

{K}

and

L

respectively. Let

{A}

and

{B}

be the points that their common tangent at point

{M}

of circles

{\omega_1}

and

{\omega_2}

intersect with circle

{\omega_3.}

Prove that if

{\angle KAB=\angle LAB}

then the segment

{AB}

is diameter of circle

{\omega_3.}

Theoklitos Paragyiou (Cyprus)

Problem Statement