A line is called a double bisector of a triangle if it divides the triangle into two polygons which have both equal areas and equal perimeters. Each polygon's perimeter includes the part of the line inside the triangle. Distinct lines are counted without orientation.
For , let be the statement:
Every non-degenerate triangle whose longest side is less than times its shortest side has exactly three double bisectors.
Which condition on is necessary and sufficient for to be true?
A
B
C
D
E