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.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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