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# A square $DEFG$ varies inside equilateral triangle $ABC$ so that $E$ always lies on side $\overline{AB},$ $F$ always lies on side

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A square $DEFG$ varies inside equilateral triangle $ABC$ so that $E$ always lies on side $\overline{AB},$ $F$ always lies on side $\overline{BC},$ and $G$ always lies on side $\overline{AC}.$ The point $D$ starts on side $\overline{AB}$ and ends on side $\overline{AC}.$ The diagram below shows the initial position of square $DEFG,$ an intermediate position, and the final position.

Show that as square $DEFG$ varies, the height of point $D$ above $\overline{BC}$ remains constant.

P.S. Can I have a non-trig solution? Thanks!

Apr 18, 2019
edited by LeoIsTheBest  Apr 18, 2019

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Here :

https://web2.0calc.com/questions/a-square-defg-varies-inside-equilateral-triangle

Apr 18, 2019
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"Can I have a non-trig solution?"

Apr 25, 2019