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May 30, 2016
Posted by **Ramesh Reddy** on Sunday, August 21, 2011 at 12:40am.

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.

- Maths -
**drwls**, Sunday, August 21, 2011 at 1:07amCall the radii r1 and r2.

The center-to-center 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 - Maths -
**Bosnian**, Sunday, August 21, 2011 at 1:32amr1= first radius

r2= second radius

r1+r2=14

r2=14-r1

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 step-by-step. - Maths -
**Bosnian**, Sunday, August 21, 2011 at 1:33amð = pi

- Maths -
**Ramesh Reddy**, Sunday, August 21, 2011 at 2:33am(14 - r2)^(14 - r2)^2 + r2^2 = 130

what is this ^ symbol represents

please explain.I cant understand it. - Maths -
**Ramesh Reddy**, Sunday, August 21, 2011 at 2:49ammadam ......please explain how did u get this step.130 pi cm^2 = pi(r1^2 + r2^2)

- Maths -
**Damon**, Sunday, August 21, 2011 at 3:28amhow 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 - Maths -
**Reiny**, Sunday, August 21, 2011 at 10:13amsimilar to drwls ......

radius of smaller -- r

radius of larger --- 14-r

πr^2 + π(14-r)^2 = 130π

r^2 + 196 - 28r + r^2 = 130

2r^2 - 28r + 66 = 0

r^2 - 14r + 33 = 0

(r-3)(r-11) = 0

r = 3 or r = 11

sub back in my definitions. - Maths -
**Sai prasanna**, Sunday, November 8, 2015 at 5:54amRadius of 1 circle = x,radius of2 circle=14-x. Now,area of circle = piR2. So,pi(x2)+pi(14-x)2=130pi. Pi(x2+196-28x+x2)=130pi. Pi at both sides is cancelled So 2x2-28x+196-130=0. 2(x2-14x+33)=0. X2-11x-3x+33=0. X(x-11)-3(x-11)=0. So, x= 3,11