In the given figure, point P is 26 cm away from the center 0 of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then, the radius of the circle is

We have given, PT is a tangent drawn at point T on the circle and OP = 26 cm and PT = 24 cm

Join OT

∴ 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}

(26)^{2} = (OT)^{2} + (24)^{2}

(OT)^{2} = 676 - 576

(OT)^{2} = 100

OT = 10 cm

Hence, radius of circle is 10 cm.

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