Question 101
Let $AB$ be a diameter of a circle $\Gamma$ and let $C$ be a point on $\Gamma$ different from $A$ and $B$. Let $D$ be the foot of perpendicular from $C$ onto $AB$. Let $K$ be a point of the segment $CD$ such that $AC$ is equal to the semiperimeter of the triangle $ADK$. Show that the excircle of triangle $ADK$ opposite $A$ is tangent to $\Gamma$.