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from a point Q, the length of the tangets to a circle with centre O so that angle POQ=110°,then angle PTO is equal to

    • Posted by Teba Habib 5 years, 1 month ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years ago

    It is given that,
    ∠POQ =110°
    Since, the Iangent at any point of a circle is perpendicular to the radius through the point of contact.
    ∴ ∠OPT = 90°
    and    ∠OQT = 90°
    Now, in quadrilateral POQT.
    ∠POQ + ∠OQT + ∠PTQ + ∠OPT = 360°
    (angle sum property of quadrilateral)
    ⇒110° + 90° + ∠PTQ + 90° = 360°
    ⇒ ∠PTQ + 290° = 360°
    ⇒    ∠PTQ = 70°

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