Theorem:A line drawn through the end point of a radius and perpendicular to it is a tangent to the circle.

Explanation

Proof `:` Take a point Q on line l , other than P.
Draw seg OQ.
In `Delta OPQ, /_OPQ = 90^(@)`
`:. Delta OPQ ` is a right angled triangle.
In a right angled triangled, the hypotenuse is the largest side.
`:. OQ gt OP `
`:. OQ gt ` radius ....( `:' OP ` = radius )
`:.` Q doesn't lie on the circle
This is true for all the points on line l, other than P
`:.` only point P is the common point between line l and the circle.
`:.` line l is tangent to the circle. ....( By definition) .