# Angle in Semicircle is Right Angle

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 .

Slope of

Slope of

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 .