Question

Two circles touch each other externally. The sum of their areas is 58πcm² and the distance between their centres is 10cm. Find the radii of the two circles​

Answer 1

Answer:

r=3cm and r=7cm

Step-by-step explanation:

Let r be the radius of one circle and,

10−r be the radius of other circle.

The area of the first circle is πr

2

The area of the first circle is π(10−r

2

)

Given,

The sum of these areas is 58πcm

2

Therefore,

πr

2

+π(10−r)

2

=58π

=>r

2

+(10−r)

2

=58 [dividing both sides by π]

=>r

2

+(10)

2

+(r)

2

−2(10)(r)=58

=>r

2

+100+r

2

−20r=58

=>2r

2

−20r+42=0

=>r

2

−10r+21=0 [dividing both sides by 2]

=>r

2

−7r−3r+21=0

=>r(r−7)−3(r−7)=0

=>(r−7)(r−3)=0

r=3cm and r=7cm

Answer 2

Answer:

Radius - 7

Radius - 3

Step-by-step explanation:

Hope this helps you !!