Q6 of 31 Page 65

In the circle of adjoining figure with its center at O, OP ⊥ AB; if AB = 6 cm. and PC = 2cm, then let us write by calculating, the length of radius of the circle.



Given, AB = 6cm, PC = 2cm


AP


Perpendicular from the center of the circle to any Chord bisects it in two line segments



⇒ AP


⇒ AP = 3cm


⇒ OA = OC


⇒ OA = OP + CP ………..(1)


In OAP, Using Pythagoras Theorem


OA2 = OP2 + AP2


⇒ (OP + PC)2 = OP2 + 9 (from eq.(1))


⇒ OP2 + PC2 + 2(OP)(PC) = OP2 + 9


⇒ PC2 + 2(OP)(PC) = 9


⇒ 4 + 2(OP)(2) = 9


⇒ 2(OP)(2) = 5


⇒ OP


Radius = OC = OP + PC


⇒ OC = 2 +


⇒ OC = 2.25cm


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