Question

two circles touch externally the sum of their areas is 130π cm and the distance between their Centre is 14 cm find the radius of the circles​

Answer 1

Answer:

Let the radius of the two circles are a and b cm

The circles touch each other externally.

So, the distance between their centers =a+b

a+b=14 ................... (1)

Sum of their areas =πa

2

+πb

2

πa

2

+πb

2

=130π

a

2

+b

2

=130 .................... (2)

From equation (1),

b=14−a ............. (3)

From (2) and (3),

a

2

+(14−a)

2

=130

a

2

+a

2

+196−28a=130

2a

2

+66−28a=0

a

2

+33−14a=0

a

2

−11a−3a+33=0

(a−11)(a−3)=0

a=3,11

If a=3, then b=14−3=11

If a=11, then b=14−11=3

So, the radius of the two circles are 3 and 11 cm

And their diameters are 6 and 22 cm.