In the given figure, O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, then the radius of the circle is _______

3.75 cm

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7.5 cm

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10.25 cm

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11.25 cm

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Solution

The correct option is D 11.25 cm
AB = 15cm, AC = 7.5cm

∠AOB = 90°, since AB is a tangent to the circle.

Let r be the radius of the circle.

Therefore, OC = OB = r

AO = AC + OC = 7.5 + r

In △AOB, AO2 = AB2 + OB2

(7.5 + r)2 = 152 + r2

$(\frac{15 + 2 r}{2})$ 2 = 225 + r2

225 + 4r2 + 60r = 900 + 4r2

60r = 900 - 225

r = $\frac{675}{60}$ = 11.25 cm.

Therefore, option d is correct.

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