Question : The radii of two concentric circles are 17 cm and 25 cm. A straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 16 cm, then the length (in cm) of PS is:
Option 1: 41
Option 2: 32
Option 3: 33
Option 4: 40
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Correct Answer: 40
Solution : Given: OQ = radius of smaller circle = 17 cm OP = radius of bigger circle = 25 cm QR = 16 cm OD is perpendicular to QR. So, QD = RD = $\frac{16}{2}=8$ cm From ∆ OQD, OQ 2 = OD 2 + QD 2 ⇒ OD 2 = $17^2-8^2$ ⇒ OD = $\sqrt{17^2-8^2}$ $\therefore$ OD = 15 cm From ∆ OPD, OP 2 = OD 2 + PD 2 ⇒ PD 2 = $25^2-15^2$ ⇒ OD = $\sqrt{25^2-15^2}$ $\therefore$ PD = 20 cm $\therefore$ PS = 2 × PD = 2 × 20 = 40 cm Hence, the correct answer is 40.
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