prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is

Question

a cos { ( alpha + beta)/2}.

Answer 1

both points are on a circle of radius a.
The distance to the line is the altitude of the triangle formed by the two points and the circle center.

Draw the diagram and see the answer checks.