construction proplem-solved pending proof

Question

ABC is a right triangle and E a point in the plane. Construct with compass and ruler the equilateral triangle EDF with D and F lying in the sides of ABC.

Answer 1

This is a complete new version.

We have to assume that E is outside of ABC and within range. Let ABC be right-angled at B.

Draw the equilateral triangle PBE.

Construct the circum-circle PBE cutting BC at X.

PX will cut AC at D.

Construct the circle (centered at E with ED as radius) cutting BC at F.

This is because if $\triangle PED \cong \triangle BEF, \angle DEF = \angle PEB = 60^0$

Answer 2

I did what you told me @Mick but as you can see the triangle is not equilateral