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.
Circles
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Answer
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 = = 11.25 cm.
Hence, radius of circle = 11.25 cm.
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