Question

two circles touch externally the sum of their area is 58pie and the distance between their centre is 10 cm find radii of each circle

Answer 1

let the radii of the be Rcm and rcm let C1 and C2 be the centre of the 2 circle, then
C1c2=R+r
R+r =10cm……………(X)
given, the sum of their area =58pi
piR^2+Pir^2=58pi
R^2+r^2=58 [pi get cancelled ]
(R+r) ^2=58……………(1)
R^2+R^2+2Rr =58
(R+r)^2=58+2Rr
10^2=58+2Rr
100-58=2Rr
2Rr =42
Rr =21
R=21/r
putting it in equation 1
(21/r)^2+r^2=58
r^4+441=58r^2
r^4-58r^2+441=0
(r^2-49) (r^2-9)=0
r^2=49,9
r=7,3
putting the value of r in equation X, we have
R=3,7
therefore the radii of the circles are 7m and 3cm respectively.

Answer 2

Answer:

Step-by-step explanation:

let the radii of the be Rcm and rcm let C1 and C2 be the centre of the 2 circle, then

C1c2=R+r

R+r =10cm……………(X)

given, the sum of their area =58pi

piR^2+Pir^2=58pi

R^2+r^2=58 [pi get cancelled ]

(R+r) ^2=58……………(1)

R^2+R^2+2Rr =58

(R+r)^2=58+2Rr

10^2=58+2Rr

100-58=2Rr

2Rr =42

Rr =21

R=21/r

putting it in equation 1

(21/r)^2+r^2=58

r^4+441=58r^2

r^4-58r^2+441=0

(r^2-49) (r^2-9)=0

r^2=49,9

r=7,3

putting the value of r in equation X, we have

R=3,7