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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
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- 41
- 32
- 33
- 40
- 41
Correct Option: D
According to question , we draw a figure of two concentric circles whose radii are 17 cm and 25 cm
Point ‘O’ is the centre of circle. OD is perpendicular on QR.
Here , QD = DR = 8 cm.
From ∆ OQD,
OD = √OQ² - QD²
OD = √17² - 8²
OD = √(17 + 8)(17 - 8)
OD = √25 × 9 = 5 × 3 = 15 cm.
From ∆ OPD,
PD = √OP² - OD²
PD = √25² - 15²
PD = √(25 + 15)(25 - 15)
PD = √40 × 10 = 20 cm.
∴ PS = 2PD = 2 × 20 = 40 cm.
