Question 68
The circles $k_1$, $k_2$ intersect at points $A$ and $B$. A line through $B$ intersects the circles $k_1$ and $k_2$ for the second time at points $C$ and $D$, respectively, in such a way that $C$ lies outside of $k_2$, and $D$ lies outside of $k_1$. Let $M$ be the point of intersection of the tangents to $k_1$ and $k_2$ drawn through $C$ and $D$, respectively, and $AM \cap CD = \{P\}$. The tangent drawn through $B$ to $k_1$ intersects $AD$ in point $L$, and the tangent drawn through $B$ to $k_2$ intersects $AC$ in point $K$. Let $KP \cap MD = \{N\}$ and $LP \cap MC = \{Q\}$. Show that the quadrilateral $MNPQ$ is a parallelogram.