ABC is a triangle. Explain how you inscribe a rhombus BDEF in the triangle such that $$D \in \overline{BC}$$, $$E \in \overline{CA}$$ and $$F \in \overline{AB}$$.

PLACEHOLDER ANSWER - the answer is a construction. Draw the bisector of $$\angle B$$ to meet CA at E. Through E draw a line parallel to AB meeting BC at D, and a line parallel to BC meeting AB at F. Then BDEF is a parallelogram whose diagonal BE bisects the angle at B, so its adjacent sides are equal and it is a rhombus.