Three identical circles are tangent to each other externally. if the area of the curvilinear formed by the point of tangency of the three circles is 142 cm2, compute the radius of each circle.

Answer 1

Let the radius of each of the equal circles be r
Joining the 3 centres will produce an equilateral triangle
The area we are given as 142 cm^2 would be
the area of that equilateral triangle - the area of the 3 sectors of
the circle contained within that triangle, so .....
area of triangle = (1/2)(2r)(2r) sin 60° = 2r^2(√3/2) = √3 r^2
the area of one of the sectors = (1/6)π r^2
so we have 3 of these , area of sectors = (1/2)π r^2

√3 r^2 - (1/2)π r^2 = 142
r^2 (√3 - π/2) = 142

you take over, let me know what you get