The given figure shows a circle with centre O in which a diameter AB bisects the chord PQ at the point R. If PR = RQ = 8 cm and RB = 4 cm, then find the radius of the circle.

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asked Dec 27, 2017 in Class IX Maths by navnit40 (-2,700 points)

The given figure shows a circle with centre O in which a diameter AB bisects the chord PQ at the point R. If PR = RQ = 8 cm and RB = 4 cm, then find the radius of the circle. 

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answered Dec 27, 2017 by ashu Premium (901 points)

Let  r be the radius, then 

OQ = OB = r and OR = (r - 4)

∴ OQ= OR + RO2  

⇒ r2 = 64 + (r-4)2

⇒ r = 64 +  r2 + 16 - 8r 

⇒ 8r = 80 ⇒ r = 10 cm 

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