IMO Shortlist 1999 problem G6
Two circles
and
touch internally the circle
in M and N and the center of
is on
. The common chord of the circles
and
intersects
in
and
.
and
intersects
in
and
. Prove that
is tangent to
.
%V0
Two circles $\Omega_{1}$ and $\Omega_{2}$ touch internally the circle $\Omega$ in M and N and the center of $\Omega_{2}$ is on $\Omega_{1}$. The common chord of the circles $\Omega_{1}$ and $\Omega_{2}$ intersects $\Omega$ in $A$ and $B$. $MA$ and $MB$ intersects $\Omega_{1}$ in $C$ and $D$. Prove that $\Omega_{2}$ is tangent to $CD$.
Source: Međunarodna matematička olimpijada, shortlist 1999
Školjka 
