MathDB
On a rectangle and lines

Source:

September 14, 2010
geometryrectanglegeometry unsolved

Problem Statement

Let ABCDABCD be a rectangle, AB=a,BC=bAB = a, BC = b. Consider the family of parallel and equidistant straight lines (the distance between two consecutive lines being dd) that are at an the angle ϕ,0≤ϕ≤90∘,\phi, 0 \leq \phi \leq 90^{\circ}, with respect to ABAB. Let LL be the sum of the lengths of all the segments intersecting the rectangle. Find:
(a) how LL varies,
(b) a necessary and sufficient condition for LL to be a constant, and
(c) the value of this constant.
Back to ProblemsView on AoPS