 ## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 1 of Exercise 12A

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##### Find the length of tangent drawn to a circle with radius 8 cm from a point 17 cm away from the center of the circle.

Let us consider a circle with center O and radius 8 cm.

The diagram is given as: Consider a point A 17 cm away from the center such that OA = 17 cm

A tangent is drawn at point A on the circle from point B such that OB = radius = 8 cm

To Find: Length of tangent AB = ?

As seen OB AB

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

In right - angled ΔAOB, By Pythagoras Theorem

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

(OA)2 = (OB)2 + (AB)2

(17)2 = (8)2 + (AB)2

289 = 64 + (AB)2

(AB)2 = 225

AB = 15 cm

The length of the tangent is 15 cm.

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