Maths
posted by Ramesh Reddy .
I am very greatefull to you if you guide me to solve this problem.
Two circles touch externally. The sum of their areas is 130π cm2 and the distance between their centers is 14 cm. find the radii of the circles?
I tried to solve this problem like this:
Area of the circle = πr2
130πcm2 = 22/7xrxr
130x22/7 =22/7xrxr
22/7xr2 =130x22/7
r2 =130x22x7/7
r2 = 130x22x7/7x22
r2 =130
r =√130
r=√2x5x13.
I tried to do this in the above way. But I couldn't get the answer further.

Call the radii r1 and r2.
The centertocenter distance is
r1 + r2 = 14
The combined area is
130 pi cm^2 = pi(r1^2 + r2^2);
therefore
130 = r1^2 + r2^2
The two equations for r1 and r2 can easily be solved by substitution.
(14  r2)^2 + r2^2 = 130
196 28r2 + 2r2^2 = 130
r2^2 14r2 + 33 = 0
(r2  11)(r2 3) = 0
The radii are 3 and 11 cm 
r1= first radius
r2= second radius
r1+r2=14
r2=14r1
The sum of circles areas is:
r1^2 * ð + r2^2 * ð = 130ð
ð * ( r1^2 + r2^2 ) = 130ð Divide both sides with ð
( r1^2 + r2^2 ) = 130
r1^2 + ( 14  r1 )^2 = 130
r1^2 + 14^2  2 * r1 *14 + r1^2 = 130
r1^2 + 196  28 * r1 + r1^2 = 130
2 * r1^2  28 * r1 + 196  130 = 0
2 * r1^2  28 * r1 + 66 = 0 Divide both sides with 2
r1^2  14 * r1 + 33 = 0
This equation have 2 solutions:
r1 = 3
and
r1 = 11
When r1 = 3
r2 = 14  r1 = 14  3 = 11
When r1 = 11
r2 = 14  r1 = 14  11 = 3
So radii is :
3 cm and 11 cm
The sum of circles areas:
3^2 * ð + 11^2 * ð =
9 *ð + 121 * ð = 130ð cm^2
P.S.
If you don't know solve equation:
r1^2  14 * r1 + 33 = 0
In google type:
Quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver: Solve by Quadratic Formula
When page be open in rectangle type:
r1^2  14 * r1 + 33 = 0
and click option solve it!
You will see solution stepbystep. 
ð = pi

(14  r2)^(14  r2)^2 + r2^2 = 130
what is this ^ symbol represents
please explain.I cant understand it. 
madam ......please explain how did u get this step.130 pi cm^2 = pi(r1^2 + r2^2)

how did u get this step.130 pi cm^2 = pi(r1^2 + r2^2)
========================
^ means "to the power"
so
r^2 = radius squared
pi r^2 = pie times radius squared
= area of circle of radius r 
similar to drwls ......
radius of smaller  r
radius of larger  14r
πr^2 + π(14r)^2 = 130π
r^2 + 196  28r + r^2 = 130
2r^2  28r + 66 = 0
r^2  14r + 33 = 0
(r3)(r11) = 0
r = 3 or r = 11
sub back in my definitions. 
Radius of 1 circle = x,radius of2 circle=14x. Now,area of circle = piR2. So,pi(x2)+pi(14x)2=130pi. Pi(x2+19628x+x2)=130pi. Pi at both sides is cancelled So 2x228x+196130=0. 2(x214x+33)=0. X211x3x+33=0. X(x11)3(x11)=0. So, x= 3,11
Respond to this Question
Similar Questions

math
Two circles with radii 3cm and r cm touch each other externally. If their common tangent is 8cm long,what is the value of r? 
maths
two circles of radii 10 cm and 17 cm intersect at two points and distance between their centers is 21 cm.find length of common chord 
Trig
Three circles with radii of 4, 5, and 6 cm, respectively, are tangent to each other externally. Find the angles of the triangle whose vertexes are the centers of the circles. 
geometry
Two circles which are not congruent touch externally. the sum of their area is 130¦Ðcm.square and distance between their centers is 14 cm. find radii of circles. 
trig
Two circles of radii 5 and 3 cm, respectively, intersect at two points. At either point of intersection, the tangent lines to the circles form a 60◦ angle, as in Figure 2.2.4 above. Find the distance between the centers of the … 
GEOMETRY
Two circles with radii a and b touch each other externally . Let c be the radius of a circle which touches these two circles as well as their common tangent to the two circles . Then relate a,b and c through an equation 
Trigonometry
Two circles, whose radii are 12 inches and 16 inches respectively, intersect. The angle between the tangents at either of the points of intersection is 29'30'. Find the distance between the centers of the circles. 
MATHS
Two circles of radii 5 cm and 12 cm are drawn, partly overlapping. Their centers are 13cm apart. Find the area common to the two circles. 
Maths
Three circles of unit radii touch each other externally. They are inscribed in triangle. What will the area after leaving the area of those circles. 
Geometry
Three circles touch one another externally.Their centres form A triangle with sides 10cm,9cm and 7cm.Find the radii of the circles