Geogebra - constructing the smallest circle that contains a triangle

Question

I want to create a Geogebra demonstration of the smallest enclosing circle of a given triangle.

The Geogebra tutorial shows how to create the circumcircle of a triangle (by calculating the intersection of the perpendicular bisectors), but, the circumcircle might be very large, there may be a much smaller enclosing circle.

A possible solution is to select the largest side of the triangle, say AB, and construct a circle that has AB as a diameter. But, I don't know how to tell Geogebra to select the largest side.

Is there another way?

Answer 1

Here it is in GeoGebra: https://www.geogebra.org/m/mWnvve4s

You can download the .ggb file to see how it was made. The tricky bits are these to select the correct center and edge points:

If[α < 90°, If[β < 90°, If[γ < 90°, O, D], E], F]

If[α < 90°, B, A]

Here's a similar construction for a square: https://www.geogebra.org/m/mkyEZsFF