Mathematics

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

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Let the radius of the circle to be r cm.

So, AO = AC + OC = (7.5 + r) cm.

In right ∆AOB, we have

⇒ AO² = AB² + OB² [By Pythagoras Theorem]

⇒ (7.5 + r)² = 15² + r²

⇒ 56.25 + r² + 15r = 225 + r²

⇒ 15r = 225 - 56.25

⇒ 15r = 168.75

⇒ r = $\dfrac{168.75}{15}$ = 11.25 cm.

Hence, radius of circle = 11.25 cm.

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