Perimeter-to-Diameter Ratio of Four Regions

For a bounded planar region, the largest distance between any two of its points is called the region's diameter, and the ratio of the length of the region's boundary curve to its diameter is called the region's perimeter ratio. The four shaded regions below are enclosed, respectively, by (parts of) a square, a circle, an equilateral triangle, and a circle (shown dashed). Their perimeter ratios, from left to right, are $\tau_1,\tau_2,\tau_3,\tau_4$. Arrange $\tau_1,\tau_2,\tau_3,\tau_4$ in increasing order.