Q. 75.0( 1 Vote )

# 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 isA. 10 cmB. 12 cmC. 13 cmD. 15 cm

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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