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Chapter 9: Q3. (page 337)

Find AB.In Exercise 3,CB炉 is tangent to 鈯�A.

Short Answer

Expert verified

The value of,AB=27.

Step by step solution

01

Step 1. Given information.

The figure here given is,

CB炉 is a tangent to circle with centre A.

02

Step 2. Concept Used.

Theorem 9.2: tangent of the circle is perpendicular to the radius of the circle.

Theorem 8.2: The Square of the hypotenuse of right triangle is equal to the sum of the squares of the sides in a right triangle.

Consider the given figure:

It is given that CB炉 is a tangent to circle with centre A.

So, by theorem 9.2,

it can be said that CB炉is perpendicular to AB炉.

That is,

m鈭�ABC=90

Let AB=x

Consider the right triangle 螖ABC.

Now, AC炉 is the hypotenuse and has length 8and the lengths of the legs are AB=x and CB=6.

So, by theorem 8.2,

AC2=AB2+BC282=x2+6264=x2+36

64鈭�36=x228=x2

03

Step 3. Now, take square root of both sides.

x2=28x=27

Therefore, the value of, AB=27.

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