PoP goes the weasel
Source: 2024 AIME I Problem 5
February 2, 2024
AMCAIMEAIME I
Problem Statement
Rectangles and are drawn such that are collinear. Also, all lie on a circle. If and what is the length of ?
[asy]
unitsize(1 cm);pair A, B, C, D, E, F, G, H;A = (0,0);
B = (5,0);
C = (5,1.5);
D = (0,1.5);
E = (1,1.5);
F = (8,1.5);
G = (8,3.5);
H = (1,3.5);draw(A--B--C--D--cycle);
draw(E--F--G--H--cycle);dot("A", A, SW);
dot("B", B, SE);
dot("C", C, SE);
dot("D", D, NW);
dot("E", E, NW);
dot("F", F, SE);
dot("G", G, NE);
dot("H", H, NW);[/asy]