Question

two circle touch each other externally. the sum of their areas is 130π and distance btw their centre is 14cm find the respective radii

Answer 1

let r1, r2 be the radii of two circles .

Area of first circle = πr1^2

Area of second circle = πr2^2

since , given that sum of their areas
= 130π

πr1^2 + πr2^2 = 130π

π ( r1^2 + r2^2 ) = 130π

r1^2 + r2^2 = 130 ------------------(1)

also given that the distance between their centres is 14cm.

r1 + r2 = 14 cm. --------------------(2)

on squaring both side ,we get

( r1 + r2 )^2 = ( 14 )^2

r1^2 + r2^2 + 2r1r2 = 196 ------(3)

by putting value of (1) in (3) , we get

130 + 2r1r2 = 196

2r1r2 = 196 - 130

2r1r2 = 66

r1r2 = 33 ---------------(4)

from (2) r2 = 14 - r1 , so now

r1 ( 14 - r1 ) = 33

14r - r1^2 = 33 => r1^2 - 14r1 + 33 = 0

r1^2 - 11r1 - 3r1 + 33 = 0

r1 ( r1 - 11 ) - 3 ( r1 - 11 ) = 0

( r1 - 3 ) ( r1 - 11 ) = 0

r1 = 3 , 11

if radius of first circle r1 =3cm then radius of second circle

r2=14 - r1= 14 - 3= 11 cm

or if radius of second circle = 11 cm then radius of first circle will be = 3 cm

therefore,

radii of two circles are 3 cm and 11cm
_______________________________
Your Answer : radii = 3 cm, 11 cm _______________________________

Answer 2

Answer:

the radii=7cm long

Step-by-step explanation:hope it will help you