Core stretch Four identical circles have centres at the vertices of a square of area \(400\text{ cm}

Question

Core stretch

Four identical circles have centres at the vertices of a square of area $400\text{ cm}^2$, and each circle is tangent to its two adjacent circles. A smaller circle at the square centre touches all four. Find its circumference to 2 decimal places.[3]

You may use the fact that the distance between the centres of two externally touching circles equals the sum of their radii.

Accepted Answer

$20\pi(\sqrt2-1)\approx26.03$ cm.

Small circle between tangent circles

Small circle between tangent circles

Solution:

Solution locked