Mathematics
The radii of two concentric circles are 17 cm and 10 cm; a line PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, calculate PQ.
Circles
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Answer
Draw OM ⊥ QR.
In right △OQM,
⇒ 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.
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