Question 51
Two circles lie completely outside each other. Let $A$ be the point of intersection of internal common tangents of the circles and let $K$ be the projection of this point onto their external common tangent. The tangents, different from the common tangent, to the circles through point $K$ meet the circles at $M_1$ and $M_2$. Prove that the line $AK$ bisects the angle $M_1KM_2$.