Annie , asked a question
Subject: Math , asked on 23/2/11

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

Abhinav Verma , added an answer, on 23/2/11
3569 helpful votes in Math

Hi Rida

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

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