Question 161
Circles $k_1$ and $k_2$, with radii $r, R$ ($r \lt R$) touch each other internally in $A$. Let $p$ be a line parallel to their common tangent and let $B$ be an intersection of the line $p$ with the circle $k_1$, and $C$ an intersection of $p$ with $k_2$, so that the points $B$ and $C$ lie on the same side of the line through the centers of given circles. Prove that the radius of the circle circumscribed to the triangle $ABC$ does not depend on the choice of line $p$. Determine that radius in terms of $r$ and $R$.