Question

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Answer 1

Draw a circle with centre O, draw a tangent PR touching circle at P.

Draw QP perpendicular to RP at a point P, QP lies in the circle.

Now,∠OPR = 90º

Also, ∠QPR = 90º 

Therefore,∠OPR = ∠QPRThis is possible only when O lies on QP.

Hence, it is proved that the perpendicular at the point of contact to the tangent to a circle passes through the centre