A point P is 25 cm away from the center of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.

Let us consider a circle with center O.

Consider a point P 25 cm away from the center such that OP = 25 cm

A tangent PQ is drawn at point Q on the circle from point P such that PQ = 24 cm

To Find : Length of radius OQ = ?

Now, OQ ⏊ PQ

[Tangent at any point on the circle is perpendicular to the radius through point of contact]

∴ In right - angled △POQ,

By Pythagoras Theorem,

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

(OP)^{2} = (OQ)^{2} + (PQ)^{2}

(25)^{2} = (OQ)^{2} + (24)^{2}

625 = (OQ)^{2} + 576

(OQ)^{2} = 49

OQ = 7 cm

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