Question 51
A circle is drawn through points $A$ and $B$ of a triangle $ABC$ such that the angle in the segment external to the triangle is the complement of $\angle ACB$. Similarly a second circle is drawn through $A$ and $C$ with the angle in the segment external to the triangle equal to the complement of $\angle ABC$.
Prove that the circles touch each other. Prove also that $BC$ is tangent to both circles when $\angle BAC = 90^\circ$.
Prove that the circles touch each other. Prove also that $BC$ is tangent to both circles when $\angle BAC = 90^\circ$.