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.
∠OPR = 90º
Also, ∠QPR = 90º
∠OPR = ∠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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