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In the given figure, PT is a tangent to the circle with center O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is
We have given, PT is a tangent drawn at point T on the circle.
∴ OT ⏊ TP
[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]
So, In △OTP we have,
By Pythagoras Theorem,
[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2]
(OP)2 = (OT)2 + (PT)2
(10)2 = (6)2 + (PT)2
(PT)2 = 100 - 36
(PT)2 = 64
⇒ PT = 8 cm