Question

The perimeter of angle ABC is 98 centimeters. If the radius circle A is twice the radius of circle C and the radius of circle B is four times the radius of circle C, then find the radius of circle C.

Answer 1

Answer : The radius of circle C is 7 cm.

Explanation:

As we shown in the figure below:

Let the radius of circle C is x

Let the radius of circle A is 2x

Let the radius of circle of B is 4x

So The length of side AC of ΔABC is x+2x = 3x

The length of side  BC  of ΔABC is 4x+x = 5x

The length of side AB of ΔABC  is 4x+2x = 6x

Since we have given that the perimeter of triangle ΔABC is 98 cm.

and we know that the perimeter means the sum of boundary of sides of triangle .

so, Perimeter = 6x+5x+3x = 98 cm

⇒ 14x= 98

⇒ x= $\frac{98}{14}$

⇒ x=7

So, the radius of circle C is 7 cm.