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Prove thata the tangent drawn at …

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Prove thata the tangent drawn at the end of the chord of a circle make equal angles with the chord

    • Posted by Vedika Roongta 4 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Raja Gupta 4 years, 9 months ago

    Yes , right answer

    0Thank You

    Yogita Ingle 4 years, 9 months ago

    Given:- A circle with center O,PA and PB are tangents drawn at ends A and B on chord AB.

    To prove:- ∠PAB=∠PBA

    Construction:- Join OA and OB

    Proof:- In △AOB, we have

    OA=OB(Radii of the same circle)

    ∠OAB=∠OBA.....(1)(Angles opposite to equal sides)

    ∠OAP=∠OBP=90(∵Radius⊥Tangent)

    ⇒∠OAB+∠PAB=∠OBA+∠PBA

    ⇒∠OAB+∠PAB=∠OAB+∠PBA(From (1))

    ⇒∠PAB=∠PBA

    Hence proved.

    0Thank You

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