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 is


A. 10 cm

B. 12 cm

C. 13 cm

D. 15 cm

Answer :


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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