MathematicsTwo tangents TP and TQ are drawn to a circle with center O from an external point T. Then ∠PTQ= ____ ∠OPQ.

Two tangents TP and TQ are drawn to a circle with center O from an external point T. Then ∠PTQ= ____ ∠OPQ.


    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    TP = TQ …(1)
    ⇒∠TQP=∠TPQ …(2)
    OP is perpendicular to TP
    ⇒∠OPT= 90
    ⇒∠OPQ + ∠TPQ= 90
    ⇒∠TPQ= 90−∠OPQ …(3)
    In triangle PTQ,
    ⇒∠TPQ + ∠PQT + ∠QTP = 180
    90−∠OPQ +∠TPQ + ∠QTP = 180
    ⇒ 2(90−∠OPQ) + ∠QTP = 180
     180−2∠OPQ + ∠PTQ = 180
    ⇒ 2∠OPQ = ∠PTQ
    ⇒ 2(90− ∠OPQ) + ∠QTP = 180
     180− 2∠OPQ + ∠PTQ = 180
    ⇒ 2∠OPQ = ∠PTQ
    Two tangents TP and TQ are drawn to a circle with center O from an external point T. Then ∠PTQ= 2∠OPQ.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.