Question

if a right angle triangle has sides of 9cm 12cm and 15 cm if two circle inscribed in it then find the radius of small circle
​

Answer 1

Answer:

area of the triangle 1/2 ×9×12 cm^2=54cm^2 ,semi perimetre of the triangle( 15 +9+12)cm/2=18cm,so radius=54/18=3cm

so, the radius of the first circle =3cm but the radius of the inner small circle can defer ,not larger than 3cm

Answer 2

Answer:

Given :-

In  Right angle ∆ABC the two small sides are 9cm and 12cm.

To Find :-

(i) radius circle. (ii)Area of shaded region.

Solution :-

Let the center of circle be O

And the onscribed circle be PQR

Now

A square may be formed as PBRO

Let the radii be r

Tagnets of circle are equal. So,

AP = AB - PE

AP = 9 - r

Also

AP = AQ

AQ = 9 - r

RC = BC - BR

RC = 12 - x

According to the question

Length of radius = AP + CP

15 = 9 - r + 12 - r

15 = 21 - 2r

15 - 21 = -2r

-6 = -2r

-6/-2 = r

6/2 = r

3 = r

Radius is 3 cm

Finding area of shaded region

Area of triangle = 1/2 × Base × Height

Area of circle = π r²

Area of shaded region = 1/2 × Base × Height - πr²

Area = 1/2 × 9 × 12 - π × (3)²

Area = 1/2 × 9 × 12 - π × 9

Area = 6 × 9 - 9π

Area = 54 - 9π

Area = 54 - 9(3.14)

Area = 25.74 cm²

[tex][/tex]