The circles within

Let the perimeters (or circumferences ) of these circles be denoted by $P1, P_2, P_3, P_4$ , where $P_1 > P_2 > P_3 > P_4$ .

And let the diamaters of these circles be denoted by $d_1, d_2, d_3, d_4$ , where $d_1 > d_2 > d_3 > d_4$ .

Then, interpreting the picture tells us that $d_1 = 20$ and $d_2 + d_3 + d_4 = 20$ .

Recall that the circumference of a circle is denoted by $\pi d$ , where $d$ represents the diameter.

The total perimeter of these 4 circles is

$\begin{aligned} P_1 + P_2 + P_3 + P_4 &=& (\pi d_1 ) + (\pi d_2 ) +(\pi d_3 ) + (\pi d_4 )\\ &=& \pi ( \; (d_1) + (d_2 + d_3 + d_4) \; ) \\ &=& \pi (20 + 20) \\ &=& 40\pi \approx \boxed{126} \quad (\text{rounded to the nearest integer}) \end{aligned}$

The technique here is to assume any number greater than 10 for the diameter of the pink circle. Now subtract that from 20, then assume any diameter for the other circles. The sum of the three diameters must be 20 cm of course. After that, compute for the perimeter of the four circles.

Simply factor out π and add the diameters to get 40. So the answer is 40π.