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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
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