Question 93

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?

Solution

Given : OP = 6.5 cm , PQ = 4.5 cm and QR = 3.5 cm

To find : Radius of circle = $$r=?$$

Solution : PM and PR are secants of the circle

=> $$(NP)\times(MP)=(PQ)\times(PR)$$

=> $$(6.5-r)(6.5+r)=(4.5)(8)$$

=> $$42.25-r^2=36$$

=> $$r^2=42.25-36=6.25$$

=> $$r=\sqrt{6.25}=2.5$$ cm

=> Ans - (C)

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