How do you construct a semicircle inside a square? Please prove your construction.?

Question

Or, may you please help me prove this one?:

Given the square ABCD.
Construct AC.
Construct ray AT that bisects angle CAD.
Label the intersection of ray AT and DC at point I.
Construct the perpendicular bisector of AI called line F.
Label the intersection of line F and segment AC at point N.
Construct circle with center N that contains A.
Label the intersections of the circle and the square at points Y and G.
Construct YG.
Semicircle YIG is the req. construction.

Answer 1

I HAVE AN IMAGE OF YOUR ANSWER
MY EMAIL IS [e-mail]
I CAN REPLY AND ATTACH IMAGE IN A DOC FILE.
IT'S EXACTLY HALF A CIRCLE LIKE THE BOTTOM HALF BUT SWUNG TO THE RIGHT 45 DEGREES

Answer 2

Your query could desire to be rephrased to invite the thank you to construct the biggest achievable semi-circle interior a sq. and prepare it rather is the biggest achievable. the 1st answer constructs a semi-circle yet no longer the biggest one. It merely reveals the middle of the sq. and constructs a circle, of which you will take a million/2. The ensuing radius is a million/2 the scale of a facet of the sq.. Your shape is for an more suitable semi-circle. It feels like it rather is the biggest yet i visit could desire to think of approximately the thank you to prepare it.