Reuleaux triangle

 

To find the radius of the circle inscribed in a Reuleaux triangle made up of arcs of a circle with a 6 cm radius, we need to understand the geometry of the Reuleaux triangle. Here are the steps:

Derivation of Formula

Final Formula:

$$r = \frac{\sqrt{3}}{6} \cdot a$$

This formula gives the radius of the inscribed circle in terms of the side length $a$ of the equilateral triangle.