MathDB

4

Part of 2022 Centroamerican and Caribbean Math Olympiad

Problems(1)

prove a rectangle it´s a square

Source: 2022 Centroamerican and Caribbean Mathematical Olympiad, P4

12/1/2022
Let A1A2A3A4A_1A_2A_3A_4 be a rectangle and let S1,S2,S3,S4S_1,S_2,S_3,S_4 four circumferences inside of the rectangle such that SkS_k and Sk+1S_{k+1} are tangent to each other and tangent to the side AkAk+1A_kA_{k+1} for k=1,2,3,4k=1,2,3,4, where A5=A1A_5=A_1 and S5=S1S_5=S_1. Prove that A1A2A3A4A_1A_2A_3A_4 is a square.
geometryrectanglesquaretangent circles