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Question
A point P is 25 cm away from the center of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
Solution
Draw a circle and let P be a point such that OP = 25cm.
Let TP be the tangent, so that TP = 24cm
Join OT where OT is radius.
Now, tangent drawn from an external point is perpendicular to the radius at the point of contact.
∴ OT ⊥ PT
In the right Δ OTP,we have:
`OP^2 = OT^2 +TP^2 ` [By Pythagoras’ theorem:]
`OT^2 = sqrt(OP^2 - TP^2 )`
`=sqrt(25^2 - 24^2`
`= sqrt(625-576)`
`=sqrt(49)`
= 7 cm
∴ The length of the radius is 7cm.
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