# two circles touching int. at A , area of shaded region = 5500 cm2 MN=7 cm Find sum of radii .the fig is two circles one big and one small touching each other internally the shadded region is...

two circles touching int. at A , area of shaded region = 5500 cm2

MN=7 cm

Find sum of radii .

the fig is two circles

one big and one small touching each other internally

the shadded region is the remaining part of bigger circle

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### 1 Answer

By data the two are is touching internally. The area of theregion between the bigger and smaller circle is 5500 cm^2. The distance between the centres of the circles is 7cm.

Therefore the distance between the centres of the circles = r2-r1, the difference of the radii of the outer and inner circles.

So r2-r1 = 7...(1)

Also the difference in areas of the outer and inner circles = pr2^2-pir1^2 which is 5500 cm^2 by data.

=> pir2^2-pir1^2 = 5500..(2).

Therefore from two we get (r^2^2-r1^2) = 5500 /pi = 1750.70.

=> r2^2-r1^2 = 1750.70.

=> (r1+r1)(r2-r1) = 1750.70.....(3).

From r1-r1 = 7. We substitute r1-r1 = 7 in (3) and get:e( r2+r1)*7 = 1750.7044.

=> r2+r1 = 1750.70/7 = 250.1006....(4).

(1)+(2): 2r2 = 7+250.1006. So r2 = 257.1006/2 = 128.5503 cm

(1) - (2): 2r1 = 250.1006-7 = 243.1006. So r1 = 243.1006/2 121.5503 cm.

Therefore the radius r2 of the outer circle is r2 = 121.5503 cm

The radius of the inner circle is r1 = 121.5503 cm.