Sorry, didn't realize ypu wanted an answer to that part.
Your construction seems to show AD and DC as perpendicular, without showing how you got them like that. With that assumption the rest of your construction looks valid,
My construction
Draw a horizontal line and using compasses, create a perpendicular bisector on it.
Draw the perpendicular bisector through the horizontal line at D, extending that line to a distance greater than 300.
Measure off a distance of 350 in the horizontal line, calling that the point C,
Set your compasses to 250 and, from D, draw an arc on the horizontal line, intersecting it at E, say.
Set your compasses to 300 and draw an arc on the vertical line, from D, intersecting it at A.
Now draw an arc, from E, cutting where the point B should be. (Using the same compasses setting of 300)
Set your compasses to 250 and draw an arc, from A, intersecting the previous arc at B.
Connect the dots.