Show that C A and C B are orthogonal?

Question

Suppose that AB is the diameter of a circle with center O and that C is a point on one of the 2 arcs joining A and B. show that CA and CB are orthogonal.

thank you for your help

Answer 1

without loss of generality let the endpoints of the diameter be (-1,0) & (1,0) and the point C be ( cos Θ, sinΘ).The vector CA = < cos Θ +1, sin Θ > and CB =< cos Θ - 1, sin Θ>. Compute CA dot CB and show it is 0. Or show that { sin Θ / [cos Θ + 1]} = - { cos Θ -1 / sin Θ}...m1 = -1/m2