Question

Two circles touch each other eternally .Their centres are at a distance of 11cm. The sum of the areas of the circles is 65 pie square cm . Find their radii​

Answer 1

Step-by-step explanation:

two circles are touch eternally,if the radii ate x cm,y cm then x-y=11

πx^2+πy^2=65π

x^2+y^2=65

(x-y)^2+2xy=65

2xy=65-11^2=65-121= -56

(x+y)^2=(x-y)^2+4xy

=121-112=9

x+y=3

x-y=11

2x=14,x=7

Answer 2

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Answer:

the radii are 7cm and 4cm

Step-by-step explanation:

a + b = 11

sum of their areas

π^2a + π^2b = 65π

a^2 + b^2 = 65

we know that b = 11 - a

a^2 + (11 - a) ^2 = 65

2a^2 - 22a + 56 =0

a^2 - 11a + 28 =0

a = 7 .......1

b = 11 - 7 = 4

the two radii are 7cm and 4cm

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