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    • Posted by Raspreet Singh 5 years, 1 month ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 1 month ago

    Let, O 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 = ∠QPR

    Now, 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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