In a triangle ABC (see the figure below)
CD is tangent to circumcircle O at C (D on AB extended) and P is
a point on the circle of center D and radius DC. AP, BP, and CP
(extended if necessary) intersect the circumcircle O at A_{1}, B_{1},
and C_{1}, respectively. Prove that C_{1}A_{1} = C_{1}B_{1}.
