What is the meaning of corner? parmenides51 wrote: Inside a right angle is given a point $A$. Construct an equilateral triangle, one of the vertices of which is point $A$, and two others lie on the sides of the corner (one on each side).

corner means angle, thanks for noticing

Given point $A$, given point $O\ =\ $x-axis $\cap\ $y-axis. $AD \bot $x-axis, $D \in\ $x-axis. Construct $AG$ with $G \in\ $x-axis, $\angle FAG=60^{\circ}$. The mirror of $G$ with respect $O$ is the point $B \in\ $x-axis. $\angle ABC=60^{\circ}$, point $C \in\ $y-axis.