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

.

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