Question

three circle of radius r touching to each other as shown in the figure find area of circle formed by touching all the three circle.​

Answer 1

Answer:

πr²/3(7-4√3)

Step-by-step explanation:

Radius of each of three circles touching each other is r.

The side of the equilateral triangle formed by joining the three centers of the given three circles = 2r

Draw a line bisecting the vertex of equilateral triangle joining the center of the inner circle.  Let R be the radius of the inner circle.

Cos30° = r/R+r

√3/2 = r/R+r

R+r = 2r/√3

√3R + √3r = 2r

=> R = (2 - √3)r/√3 is the radius of the small circle touching all the three circles.

Area of smaller circle = πR² = π[(2 - √3)r/√3]² = πr²/3(7-4√3)

Hope this answer's your question.