# Angle in Semicircle is a Right Angle

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 .

Slope of

Slope of

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 .