Passing through each other's centers

In the figure, since the circles are identical, they have same radius.

So $\Delta PFB, \Delta PBD,\Delta PGD$ are equilateral.

Therefore angle $GPF=180$

So Arc FG is a semicircle of perimeter $\frac{1}{3}\times12=4$

Therefore the circumference of any one of the 3 identical circles is $\boxed 8$ .

Because all circles pass through each other's centers, the total perimeter consists of 3 half circles, so a half circle is 12/3 = 4. The whole perimeter of 1 circle must be 8.

$\text{as,all circles pass through each others centers,the total perimeter is actually for }$ $\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{3}{2}$ $\text{circles}$

$\text{we know that ,the perimeter of a circle is}$ $=2τr$

$\text{now,}$

$2τr \times \frac{3}{2}=12$

or, $2τr=12 \times \frac{2}{3}$ = $8$ square unit. .............[answer]

As the circles pass through each others centres, the intersection of any two circles that is not on the bold line must be the centre of a third circle.

As a result, the bold line is 3 semi-circles, having a perimeter of 12. Therefore the circumference of each circle is (12/3)*3 = 8.

https://sciencevsmagic.net/geo/#0A1.1A0.2A0.3L4

The line here is drawn from the intersection points of the other two circles. That it goes through the center, and is therefore a diameter, gives us a crucial step: each circle is contributing half of its circumference to the circumference of the whole shape. There are three circles. The rest is left as an exercise for the reader.

The figure can be drawn with three regular hexagons inscribed within each circle part, the middle most equilateral triangle (1/6 of the regular hexagon) shared between all the triangles, and the three that share an edge with the central most triangle are shared between two of the hexagons.

Remaining, each overlapped circle has their separate 1/2 hexagon (with outer perimeter (ignoring the flat surface that it has been halved across) also half that of the full hexagon). Because these outer half hexagons are inscribed in the circle, and are regular, we notice that the part of the circle (which is included in the perimeter which = 12) starts and ends at what we now know are opposing points of the hexagon, (or vertices of the equilateral triangle we formed by adding three congruent triangles to the centre most one) so is a semi circle.

We can now do:

12/3 (Full perimeter/ Parts of that perimeter) = 4, which is the curved edge of the semi circle (half of the full circle), so 4*2 which =8

Hence 8

The three circles are identical, so you can split the total perimeter of the thick line into three. 1. 12/3 = 4 Then, I assumed that half of one circle’s circumstance is thick and half is thin, so I multiplied my result by 2 to receive my answer. 2. 4x2= 8 8 is the circumstance of one identical circle

Just imagine my sayings

From the given diagram just remove one circle form bottom two, and in mirror see them now you can see that the circles on the thicker side are half circles

My clumsy solution is this: The thicker perimeter consists of 3 halves of the circumference of the circles (c), so 3/2c=12. Therefore the circumference of 1 circle is 12÷3/2=8

As the shape is symmetrical, the perimeter can be divided into 3 equal semicircles each having perimeter = 4. So circumference of any circle is 2*4=8

because all the circles are passing through each other's centers so that they cut the circumference of each other into half that's why we have the total circumference 1/2+1/2+1/2=3/2 3/2 of circumference is 12 so that 2/3*12=8 is the right answer

3 1/2 circles totaling 12 divided by 3 equals 4 x 2 equals 8

2(12/3) or 12*2/3

As the perimeter is sum of three semicircles so r comes out to be14/11 then using 2pi r we getthe answer 8