Question

3 circles each of radius 1 cm touch each other externally. Find the ratio of area trapped between the circles to the total area of 3 circles.
Please answer ASAP.​

Answer 1

Answer:

Step-by-step explanation:

Construct an equilateral triangle using the radii of the circles (Refer to attachment)

In the triangle we notice that the circle inscribes 3 sectors within the triangle. The central angle of these sectors is 60 degrees (Angles of equilateral triangles are 60 degrees)

Therefore area of each sector will be:

$\frac{60}{360}$ * π * r²

= π/6

Therefore of area of three sectors will be: π/2

Now area of equilateral triangle is: √3/4 * a²

= √3/4 * (2r)²

= √3 r² = √3

Area of shaded region = Area of triangle - Area of sectors = √3 - π/2 .......(i)

Now area enclosed by each circle = π*r² = π

Area enclosed by 3 circles is 3π................................(ii)

Ratio = $\frac{(i)}{(ii)}$

         =$\frac{\sqrt{3} - \pi  }{\pi }$

Now, you can multiply and divide numerator and denominator accordingly to produce required result.

Hope this helps!

Forgive silly mistakes :P