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

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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