Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center?

Draw a circle with centre O.

draw a tangent PR touching circle at P.

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

Now, angle OPR = 90 degree (radius perpendicular to tangent)

also angle QPR = 90 degree (given)

Therefore angle OPR = angle QPR. This is possible only when O lies on QP. Hence, it is prooved that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Answer By- Rajendra Meena, Jaipur, India. email: rajendra.meena21@gmail.com