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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