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Question

In the figure, the diameter CD of a circle with centre O is perpendicular to the chord AB. If AB = 12 cm and CE = 3 cm, find the radius of the circle (in cm)

 


Solution

Join OA. 

Since, perpendicular drawn from the centre of circle to a chord, bisects the chord

 

AE = EB = 6 cm

Let r be the radius of the circle. Then, OA = OC = r cm

OE = (OC – CE) = (r – 3) cm.

 In right-angled DOEA, we have

OA2 = AE2OE2                     [By Pythagoras Theorem]

r2 = 62(r3)2                          [OA = r cm, AE = 6 cm & OE = (r – 3) cm]

r2r2 + 36 - 6r +9

6r = 45

r = 7.5

Hence, the radius of the circle is 7.5 cm.

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