Školjka

%V0 Given an oriented line $\Delta$ and a fixed point $A$ on it, consider all trapezoids $ABCD$ one of whose bases $AB$ lies on $\Delta$, in the positive direction. Let $E,F$ be the midpoints of $AB$ and $CD$ respectively. Find the loci of vertices $B,C,D$ of trapezoids that satisfy the following: (i) $|AB| \leq a$ ($a$ fixed); (ii) $|EF| = l$ ($l$ fixed); (iii) the sum of squares of the nonparallel sides of the trapezoid is constant. Remark Remark. The constants are chosen so that such trapezoids exist.