Consider the regular $101$-gon. A line $l$ does not contain any vertex of this polygon. Prove that line $l$ intersects even number of the diagonals of this polygon.
Source: Polish Junior MO 2019 Second Round
Tags: combinatorics
Consider the regular $101$-gon. A line $l$ does not contain any vertex of this polygon. Prove that line $l$ intersects even number of the diagonals of this polygon.