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    Question

    In a circle, two tangents PA and PB are drawn from an

    external point P such that the angle āˆ  APB = 60Ā°. If the radius of the circle is 10 cm, find the length of each tangent.
    A 10 cm Correct Answer Incorrect Answer
    B 10āˆš3 cm Correct Answer Incorrect Answer
    C 20 cm Correct Answer Incorrect Answer
    D 5āˆš3 cm Correct Answer Incorrect Answer

    Solution

    In a circle, the tangents drawn from an external point are equal in length. Let the length of the tangent be x cm. In triangle āˆ†APB, since PA = PB, āˆ†APB is an isosceles triangle. Also, āˆ  APB = 60Ā°. Using the cosine rule: xĀ² = 10Ā² + 10Ā² āˆ’ 2(10)(10)cos(60Ā°) xĀ² = 100 + 100 āˆ’ 200 Ɨ (1/2) xĀ² = 200 āˆ’ 100 xĀ² = 100 x = 10 cm Correct answer: a) 10 cm

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