Question 80
For a convex hexagon $ABCDEFG$, three triangles $ABC$, $CDE$, $EFA$ are similar. That is,
$$
\angle BAC = \angle DCE = \angle FEA
$$
$$
\angle BCA = \angle DEC = \angle FAE.
$$
Find conditions on these three triangles under which $\triangle ACE$ is an equilateral triangle if and only if $\triangle BDF$ is an equilateral triangle.
$$
\angle BAC = \angle DCE = \angle FEA
$$
$$
\angle BCA = \angle DEC = \angle FAE.
$$
Find conditions on these three triangles under which $\triangle ACE$ is an equilateral triangle if and only if $\triangle BDF$ is an equilateral triangle.