Lesson Three circles touching externally

Three circles touching externally

Problem 1

When two circles touch externally, the distance between their center is the sum of their radii.

It gives you the system of three equations

a + b = 3,     (1)
a + c = 4,     (2)
b + c = 3.     (3)

where a, b and c are the radii of the three circles with the centers A, B and C respectively.


To solve the system, first add all the three equations. You will get

2a + 2b + 2c = 3 + 4 + 3 = 10,

which implies 

a + b + c = 5.   (4)


Now extract equation (3) from equation (4) (both sides). You will get a = 5-3 = 2.

    Extract equation (2) from equation (4) (both sides). You will get b = 5-4 = 1.

Finally, extract equation (1) from equation (4) (both sides). You will get a = 5-3 = 2.

Answer.  The radii are: 2 cm for the circle with the center at A;
         1 cm for the circle with the center at B;
         2 cm for the circle with the center at C.