# 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 isA. 8 cmB. √104 cmC. 12 cmD. √125 cm

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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