Consider the equation of the circle with centre at the origin is given by the equation
Let be nay diameters of the circle and be any point on the given circle.
We shall show that .
Suppose that coordinates of is , then has coordinates .
Now multiplying the slopes and , we get
Since points and lies 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 .