Consider the equation of the circle with the center at the origin is given by
Let be any diameter of the circle and be any point on the given circle.
We shall show that .
Suppose that coordinates of are , then has coordinates .
Now multiplying the slopes and , we get
Since points and lie on the circle, we have
Substituting the values of and from equation (ii) into equation (i), we get
This is the condition of perpendicular lines. Thus and so .