SSC CGL Tier II 12 Apr 2015 Paper

Question : 30 of 100

Marks: +1, -0

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

Validate

Solution:

(4)

Point ‘O’ is the centre of circle.
OD is perpendicular on QR.
QD = DR = 8 cm.
From ΔOQD,

{OD}=√{ {OQ}^{2}- {QD}^{2}}

=√{17^{2}-8^{2}}

=√{(17+8)(17-8)}

=√{25 × 9}=5× 3=15 {cm}

From ΔOPD,

P D=√{O P^{2}-O D^{2}}

=√{25^{2}-15^{2}}

=√{(25+15)(25-15)}

=√{40× 10}=20 {cm}

∴ P S=2 P D=2 × 20=40 {cm}

Go to Question:

Prev Question

Next Question