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**Tangent to a Circle **

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

NOTE:I. There is only one tangent at a point of the circle.

II. The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.

**Theorem 1 **

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 âŠ¥ XY

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