Question
In a circle of radius 5 cm, a point P lies outside the
circle at a distance 13 cm from the centre O. Tangents PA and PB are drawn from P to the circle, touching at A and B. Find the length of chord AB.Solution
OP = 13, OA = OB = 5 Right triangle OAP: AP² = OP² − OA² = 13² − 5² = 169 − 25 = 144 ⇒ AP = 12 cm ∠OAP is angle between OP and AP. sin∠OAP = opposite/hypotenuse = AP/OP = 12/13 Angle at centre subtended by chord AB is ∠AOB = 2∠OAP. Chord length formula: AB = 2r sin(∠AOB/2) = 2r sin(∠OAP) So AB = 2 × 5 × (12/13) = 120/13 cm.
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