Question 69
Given a convex $2n$-gon $H$ with pairwise parallel opposite sides.
a) Prove that there exists a pair of the opposite sides of $H$ which possesses the following property: there exists a straight line that is perpendicular to these sides and intersects each of them.
b) Are there any values of $n$ such that for a convex $2n$-gon there exist two pairs of its opposite sides for each of which the property described in a) holds?
a) Prove that there exists a pair of the opposite sides of $H$ which possesses the following property: there exists a straight line that is perpendicular to these sides and intersects each of them.
b) Are there any values of $n$ such that for a convex $2n$-gon there exist two pairs of its opposite sides for each of which the property described in a) holds?