Question

Two circles touch internally. The sum of thier area is 116 π cm. Distance between thier center is 6 cm. Find the radii.

Answer 1

Answer:

Step-by-step explanation:

Given: the distance between centres =6

Since, they are internally touching circle we have to subtract the radii

Let, first circle's radii be x and the another one be y.

Therefore we get x-y=6. .......(1)

Now we have the second condition as there area's sum is 116π.

So we have to add their areas.

πx^2 + πy^2=116π

Now take π as common.

π(x^2+y^2)=116π

x^2+y^2=116 ...(2)... Dividing each side by π

We have x-y=6

So we can get x=6+y

Substitute it into equation (2)

We get (6+y)^2 + y^2 =116

When we expand it we get

36 + y^2+ 12y + y^2=116

When we solve it we get

2y^2 + 12y - 80=0

Divide it by 2

So we get,

Y^2 + 6y - 40

After solving quadratic equation we get,

y= 4 or y= -10

But as y is distance it can't be negative

Therefore,y = 4 is acceptable

So after putting y=4 in x - y=6

We get x = 10 and y = 4

Hope you leave 5. Star for my answer