Ethan is using his compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is he in the process of constructing?

Question

prince1342 · Answer

attachment

prince1342 · Answer

An equilateral triangle
 A square
 A regular pentagon
 A regular hexagon

michele_laino · Answer

hint:
the two little red arcs have been made using the distance OA as radius

prince1342 · Answer

Hmm. I think it might be a square

michele_laino · Answer

now, we can see that the distances OM, ON, and OP are equals each to other:

michele_laino · Answer

so, what can you conclude?

prince1342 · Answer

Come to think of it,, it looks like it can be a triangle. When connecting the letters you name it looks like it could be

michele_laino · Answer

more precisely, we can say that the triangles OMP, OMN, ONP, are all isosceles triangles with  congruent sides, in particular we have 
PM is congruent to MN, MN is congruent to PN, and PN is congruent to PM

prince1342 · Answer

Thank you!!!

michele_laino · Answer

:)