Balancing the Cooking Pot

The photo below is from the Field Institute Office of the Azim Premji Foundation, Puducherry. Use the geogebra sketch to answer a practical question.
This photo appeared in issue II-1 of the high school mathematics resource At Right Angles published by the Azim Premji University and the Community Mathematics Centre. You can access the magazine at http://teachersofindia.org/en/atria Suppose you were lighting a fire in this space and cooking something -what would be the smallest radius of a circular cooking vessel placed on these stones? (Any smaller and your vessel would fall in!) Clearly we need to get the radius of the circle which touches all three sides of the triangle. The radius of the vessel needs to be greater than the radius of this circle! What is this type of circle called? How can it be constructed? How is the radius of this circle related to the side of the triangle?