In a regular polygon with 100 vertices, 10 vertices are painted blue, and 10 other vertices are painted red. 1. Prove that there exist two distinct blue vertices \( A_1 \) and \( A_2 \), and two distinct red vertices \( R_1 \) and \( R_2 \), such that the distance between \( A_1 \) and \( R_1 \) is equal to the distance between \( A_2 \) and \( R_2 \). 2. Prove that there exist two distinct blue vertices \( A_1 \) and \( A_2 \), and two distinct red vertices \( R_1 \) and \( R_2 \), such that the distance between \( A_1 \) and \( A_2 \) is equal to the distance between \( R_1 \) and \( R_2 \).