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      Question

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

      external point P such that the angle ∠ 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 10√3 cm Correct Answer Incorrect Answer
      C 20 cm Correct Answer Incorrect Answer
      D 5√3 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 ∆APB, since PA = PB, ∆APB is an isosceles triangle. Also, ∠ APB = 60°. Using the cosine rule: x² = 10² + 10² − 2(10)(10)cos(60°) x² = 100 + 100 − 200 × (1/2) x² = 200 − 100 x² = 100 x = 10 cm Correct answer: a) 10 cm

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