Question

The circles having radii 1,2,3 touch each
other externally then the radius of the
circle which cuts the three circles
orthogonally is​

Answer 1

Given: The circles having radii 1,2,3 cm

To find: The radius of the  circle which cuts the three circles  orthogonally?

Solution:

• Now the radius is given as 1 cm, 2 cm, 3 cm. So the triangle formes will have sides as follows:

                (1 + 2) cm, (2 + 3)cm and (1 + 3) cm

                which is 3 cm, 5 cm and 4 cm.

• Now according to Heron's formula, we have:

                area = √ { s(s - a)(s - b)(s - c) }

• Let s be semi-perimeter, then:

                s = (a+b+c)/2

• Now putting values in s, we get:

                s = (3+4+5)/2

                s = (8+4)/2

                s = 12/2

                s = 6

• Now putting values in area, we get:

                Area = √ { 6 x (6 - 3) x (6 - 4) x (6 - 5) }

                Area = √ { 6 x 3 x 2 x 1 }

                Area = √ { 6 x 6 }

                Area = 6

• Now we know that circum radius of triangle is:

                abc / ( 4 A )

• So:

                Circum radius = (3 x 4 x 5) / (4 x 6)

                                           ( 3 x 5 )/6

                                           5/2

                                           2.5 cm

Answer:

             The radius of the  circle which cuts the three circles  orthogonally is 2.5 cm.