SSC CGL Model Paper 14

Question : 68 of 100

Marks: +1, -0

P is a point outside the circle at distance of 6.5 cm from centre O of the circle. PR be a secant such that it intersects the circle at Q and R. If PQ = 4.5 cm and QR = 3.5 cm, then what is the radius (in cm) of the circle ?

Validate

Solution:

According to the question,

(SP)^2 = P Q×P R

= P Q [PQ + QR]

= 4.5[4.5 + 3.5] =36

∴ SP = 6
In ΔOSP,

(OS)^2 =(O P )^2 -(S P )^2

= (6.5)^2 - (6 )^2 =6.25

∴ OS

=√6.25=2.5\cm

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