Question 8
(ROM 2) 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) $|AB|\le a$ ($a$ fixed);
(ii) $|EF|=l$ ($l$ fixed);
(iii) the sum of squares of the nonparallel sides of the trapezoid is constant.
Remark. The constants are chosen so that such trapezoids exist.
(i) $|AB|\le a$ ($a$ fixed);
(ii) $|EF|=l$ ($l$ fixed);
(iii) the sum of squares of the nonparallel sides of the trapezoid is constant.
Remark. The constants are chosen so that such trapezoids exist.