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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?

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? Correct Answer 2.5

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Let the perpendicular bisector from centre of circle to the cord be C

Now in triangle OCP, Using Pythagoras theorem

⇒ OP2 = OC2 + CP2

⇒ OC2 = 6.52 - (4.5 + 3.5/2)2       ----(i)

Now in triangle COR, using Pythagoras theorem

⇒ OR2 = radius2 = (3.5/2) 2 + OC2 From (i)

⇒ radius2 = 1.752 + 6.52 - (4.5 + 3.5/2) 2

⇒ radius2 = 6.25

⇒ radius = 2.5

∴ The radius is 2.5 cm

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