The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, find the length PQ.
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Question

The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, find the length PQ.

KnowledgeBoat · Accepted Answer

Draw OM ⊥ QR. Since, perpendicular from center bisects the chord. Thus, QM = = 6 cm. In right △OQM, By pythagoras theorem, ⇒ OQ2 = OM2 + QM2 ⇒ 102 = OM2 + 62 ⇒ OM2 = 100 - 36 ⇒ OM2 = 64 ⇒ OM = = 8 cm. In right △POM, ⇒ PO2 = OM2 + PM2 ⇒ 172 = 82 + PM2 ⇒ PM2 = 289 - 64 ⇒ PM2 = 225 ⇒ PM = = 15 cm. From figure, PQ = PM - QM = 15 - 6 = 9 cm. Hence, PQ = 9 cm.

Mathematics

The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, find the length PQ.

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