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Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center. |
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Answer» is the centre of the given circle.A tangent PR has been drawn touching the circle at point P.Draw QP ⊥ RP at point P, such that point Q LIES on the circle.∠OPR = 90° (RADIUS ⊥ tangent)Also, ∠QPR = 90° (Given)∴ ∠OPR = ∠QPRNow, the above case is possible only when centre O lies on the LINE QP.Hence, perpendicular at the point of CONTACT to the tangent to a circle passes through the centre of the circle. |
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