Mathematics
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.
Circles
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Answer
Let a circle be with centre O and radius 8 cm.
Let P be an external point from where a tangent is drawn to meet the circle at T.
∴ OP = 10 cm and OT = 8 cm
We know that,
The tangent at any point of a circle and the radius through this point are perpendicular to each other.
In right ∆OTP, we have
⇒ OP2 = OT2 + PT2 [By Pythagoras Theorem]
⇒ 102 = 82 + PT2
⇒ PT2 = 100 - 64 = 36
⇒ PT = 6 cm.
Hence, the length of tangent = 6 cm.
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