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14. The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts the largercircle at P and S and the smaller circle at Q and R. If QR 12 cm, find the length PQ |
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Answer» Given OP = 17 cm and OR =OQ = 10 cm QR = 12 cm(We have interpreted R=12 cm as QR=12cm) To find PQ: Drop OM perpendicular to QR. Since perpendicular from center to chord bisects the chord MQ = 6 cm In triangle OMQ, MQ = 6 cm, OQ = 10cm Using Pythagoras theorem OM = square root (100 – 36) = square root (64) = 8 In triangle OMP, OM = 8 cm, OP = 17 cm using Pythagoras theorem PM = square root (289 – 64) = square root (225) = 15 cm Clearly PQ = PM – QM = 15 cm – 6 cm = 9 cm |
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