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Question
Find the length of tangent drawn to a circle with radius 8 cm form a point 17 cm away from the center of the circle
Solution
Let O be the center of the given circle.
Let P be a point, such that
OP = 17 cm.
Let OT be the radius, where
OT = 5cm
Join TP, where TP is a tangent.
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:]
`TP = sqrt(OP^2 - OT^2)`
`=sqrt(17^2 -8^2)`
` =sqrt(289-64)`
`= sqrt(225)`
= 15 cm
∴ The length of the tangent is 15 cm.
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