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Prove that perpendicular at point of …

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Prove that perpendicular at point of contact to tangent to circle passes through centre. ????Any one Help . Please tell

    • Posted by Abc Def 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Let APB be the tangent and take O as centre of the circle.

    Let us suppose that MP{tex}\bot{/tex}AB does not pass through the centre.
    Then,
    {tex}\angle OPA = 90^\circ{/tex} [{tex}\because{/tex} Tangent is perpendicular to the radius of circle]
    But {tex}\angle MPA = 90^\circ{/tex} [Given]
    {tex}\therefore \angle OPA = \angle MPA{/tex}
    This is only possible when point O and point M coincide with each other.
    Hence, the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

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