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Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60° Q.4

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What is the best and the simple way to solve the problem of question 4 of Constructions of exercise 11.2 of class 10th math, suggest me the simple way to solve this problem Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°

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  1. Construction Procedure:

    The tangents can be constructed in the following manner:

    1. Draw a circle of radius 5 cm and with centre as O.

    2. Take a point Q on the circumference of the circle and join OQ.

    3. Draw a perpendicular to QP at point Q.

    4. Draw a radius OR, making an angle of 120° i.e(180°−60°) with OQ.

    5. Draw a perpendicular to RP at point R.

    6. Now both the perpendiculars intersect at point P.

    7. Therefore, PQ and PR are the required tangents at an angle of 60°.

    Ncert solutions class 10 Chapter 11-12

    Justification:

    The construction can be justified by proving that ∠QPR = 60°

    By our construction

    ∠OQP = 90°

    ∠ORP = 90°

    And ∠QOR = 120°

    We know that the sum of all interior angles of a quadrilateral = 360°

    ∠OQP+∠QOR + ∠ORP +∠QPR = 360o

    90°+120°+90°+∠QPR = 360°

    Therefore, ∠QPR = 60°

    Hence Justified

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