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Find the length of tangent drawn to a ci...

Find the length of tangent drawn to a circle of radius 6 cm, from a point at a distance of 10 cm from the centre.

Text Solution

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Since tangent is perpendicular to the radius through the point of contact
`:.` ` angleOTP=90^(@)`
In right triangle OTP, we have
`OP^(2)=OT^(2)+PT^(2)`
`implies` `10^(2)=6^(2)+PT^(2)`
`implies` `PT^(2)=100-36=64`
`implies` `PT=8cm`
Hence, length of tangent is 8 cm.
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