Constructing figures in dynamic geometry—like the inscribed triangles—requires thinking about dependencies among points, segments and circles. You can talk about these dependencies in the form of proofs, which explain why the relationships among the points, segments and circles are always, necessarily true, even when any of the points are dragged around.
Many proofs in geometry involve showing that some triangles are congruent to others. You can prove that the inscribed triangles are equilateral by proving that certain triangles are congruent to each other. Chat about what you can prove and how you know that certain relationships are necessarily true in your figure. Explain your proof to your team. Does everyone agree?
If you have not studied congruent triangles yet, then you may not be able to complete the proof. Come back to this after you study the activities on congruent triangles.