Question

The three circles A, B, C with the center touch each other externally. If AB is equal to 5 cm, BC is equal to 7 cm and CA is equal to 6 cm, then what is the length of the radius of the circle centered A?​

Answer 1

so radius of circle A is 2 cm

Answer 2

Given:

AB = 5cm

BC = 7cm

CA = 6cm

To find:

The length of the radius of the circle centered A.

Solution:    

Now, we will assume the equation

X + Y = 5  ⇒Equation 1

Y +Z = 7    ⇒Equation2

Z +X = 6    ⇒Equation 3

Here, we need to add the equation 1 , 2 and 3.

We get,

2 (X + Y+ Z) = 5 + 7 +6

2 (X +Y+Z) = 18

X + Y +Z = 9    ⇒Equation 4

Now, we will equate the equation (2) and (4)

Y + Z = 7 = X +Y +Z =9

Y + Z -X - Y- Z = 7- 9

X = 2

Therefore the radius of the circle R is 2cm.

The length of the radius of the circle centered A is 2cm.