Circles-Notes

•   Tangent to a Circle

       A tangent to a circle is a line that touches the circle at only one point.

The tangent at any point of a circle is perpendicular to the radius, through the point of contact.

Proof: We have the centre O of the given circle and XY is the tangent to the circle at a point P.

Let us take a point Q on Xy other than P, Join OQ.

Obviously, Q lies outside the circle.

i.e., OQ > OP

Since, all the points on XY, except P lies outside the circle.

i.e., OP is smaller than all the distance of the point O from XY.

i.e., OP is the smallest distance of O from XY.

i.e., OP ⊥ XY