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    Question

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

    external point P such that the angle тИа APB = 60┬░. If the radius of the circle is 10 cm, find the length of each tangent.
    A 10 cm Correct Answer Incorrect Answer
    B 10тИЪ3 cm Correct Answer Incorrect Answer
    C 20 cm Correct Answer Incorrect Answer
    D 5тИЪ3 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 тИЖAPB, since PA = PB, тИЖAPB is an isosceles triangle. Also, тИа APB = 60┬░. Using the cosine rule: x┬▓ = 10┬▓ + 10┬▓ тИТ 2(10)(10)cos(60┬░) x┬▓ = 100 + 100 тИТ 200 ├Ч (1/2) x┬▓ = 200 тИТ 100 x┬▓ = 100 x = 10 cm Correct answer: a) 10 cm

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