Q. 315.0( 2 Votes )

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the center of the circle is
A. 8 cm

B. √104 cm

C. 12 cm

D. √125 cm

Answer :


Let us consider a circle with center O and TP be a tangent at point A on the circle, Joined OT and OP


Given Length of tangent, TP = 10 cm, and OT = 5 cm [radius]


To Find : Distance of center O from P i.e. OP


Now,


OP TP


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


So OPT is a right - angled triangle,


By Pythagoras Theorem in ΔOPB


[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2 ]


(OT)2 + (TP)2 = (OP)2


(OP)2 = (5)2 + (10)2


(OP)2 = 25 + 100 = 125


OP = √125 cm

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