Question

distance
The circles which cire not congruent
louch externally. The sum of their areas
is 130 Tcm² and distance between
their centres is 14cm. Find the radii
of the two circles As
4​

Answer 1

Step-by-step explanation:

Let R1 and R2 be the radii of the two circles having centers A and B.

Given:

sum of areas of two circles =130πcm²

distance between their centers =14cm

Area of circle = π*R²

πR1² + πR2²= 130πcm²

R1²+R2²=130 --------(1)

Distance between their centers =14 cm

R1+R2= 14 cm -----------(2)

on sq. both sides ,

(R1+R2)² =(14)²

R1²+R2²+2R1R2= 196

130+2R1R2=196

R1R2=33 -------------(3)

(R1-R2)²=(R1+R2)²-4R1R2

(R1-R2)²=196-4(33)

(R1-R2)²=64

R1-R2= √64

R1-R2=8 -----------(4)

on solving equation (2) and (4)

R1+R2=14

R1-R2=8

----------------

2R1=22

R1 =11

putting the value of R1 in eq.(4)

R1-R2=8

11-R2=8

R2=3

R2=3 cm and R1= 8 cm

HOPE THIS HELPS YOU