Euclidea 4.9

Euclidea 4.9 Square by midpoints on opposite edges


Given the mid-points on opposite edges, $${\rm A} $$, $${\rm B} $$, make a square.

Goal: 6L, 10E 

Solution 10E (a)
There are two different 10E solutions, both very interesting. Let's start with one.




 * 1) Center $$ {\rm A} $$, radius $$ \overline{\rm AB} $$ draw circle;
 * 2) Center $$ {\rm B} $$, radius $$ \overline{\rm BA} $$, draw circle to intersect $$ \odot {\rm A} $$ at points  $$ {\rm C, D} $$;
 * 3) Connect $$ \overline{\rm CB} $$, intersect $$ \odot B $$ at $$ {\rm E} $$;
 * 4) Connect $$ \overline{\rm EA} $$, intersect $$ \odot A $$ at $$ {\rm F, G} $$;