MathDB
Find the loci of vertices B,C,D of trapezoids

Source:

September 23, 2010
geometrytrapezoidparallelogramrectangleIMO Shortlist

Problem Statement

Given an oriented line Δ\Delta and a fixed point AA on it, consider all trapezoids ABCDABCD one of whose bases ABAB lies on Δ\Delta, in the positive direction. Let E,FE,F be the midpoints of ABAB and CDCD respectively. Find the loci of vertices B,C,DB,C,D of trapezoids that satisfy the following:
(i) ∣AB∣≤a|AB| \leq a (aa fixed);
(ii) ∣EF∣=l|EF| = l (ll fixed);
(iii) the sum of squares of the nonparallel sides of the trapezoid is constant.
[hide="Remark"]
Remark. The constants are chosen so that such trapezoids exist.
Back to ProblemsView on AoPS