Q. 34.5( 2 Votes )

In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the center of the circle, then length OP = ?


A. 30 cm

B. 28 cm

C. 25 cm

D. 18 cm

Answer :

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


(OP)2 = (7)2 + (24)2


(OP)2 = 49 + 576


(OP)2 = 625


OP = 25 cm

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