Math, asked by geetapathrabe4, 3 months ago

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Answered by tennetiraj86
2

Answer:

Third Option

Step-by-step explanation:

Given :-

AB = 15 cm and AC = 7.5 cm

To find :-

Find the radius of the circle ?

Solution :-

Given that

O is the centre of the circle.

AB is the tangent .

AB = 15 cm

AC = 7.5 cm

and

Radius of the circle = OB = OC = OD

Let the radius be r cm

OB = OC = OD = r cm

Join O and B

We know that

The angle between the radius and the tangent drawn from the external point to the circle at the point of contact is 90°

We have ,

∆ OAB is a right angled triangle,

OA is the hypotenuse.

By Pythagorous Theorem,

OA² = OB² + AB²

We have, OA = OC + CA

=> (OC+CA)² = OB²+AB²

=> (r+7.5)² = r²+15²

=> r²+2(r)(7.5)+(7.5)² = r²+225

Since (a+b)² = a²+2ab+b²

Where, a = r and b = 7.5

=> r²+15r+56.25 = r²+225

In cancelling r² both sides then

=> 15r+56.25 = 225

=> 15r = 225-56.25

=> 15r = 168.75

=> r = 168.75/15

=> r = 11.25 cm

Therefore, radius = 11.25 cm

Answer:-

The radius of the given circle is 11.25 cm

Used formulae:-

→ The angle between the radius and the tangent drawn from the external point to the circle at the point of contact is 90°.

Pythagoras theorem:-

" In a right angled triangle, The square of the hypotenuse is equal to the sum of the squares of the other two sides".

→ The side opposite to the right angle in a right angled triangle is its hypotenuse.

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