RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 2 of Exercise 12A

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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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