AMC 8 2026 (Problem 23)Lakshmi has 5 round coins of diameter 4 centimeters. She arranges the coins in 2 rows on a table top, as shown below, and wraps an elastic band tightly around them. In centimeters, what will be the length of the band?(A) 2π+20\text{(A)}\;2\pi+20(A)2π+20(B) 52π+20\text{(B)}\;\frac{5}{2}\pi+20(B)25π+20(C) 4π+20\text{(C)}\;4\pi+20(C)4π+20(D) 92π+20\text{(D)}\;\frac{9}{2}\pi+20(D)29π+20(E) 5π+20\text{(E)}\;5\pi+20(E)5π+20Related TopicsToolkit 54 — Area Formulas and Important Geometry FormulasToolkit 68 — Circles, Tangents, and Radical AxisHints (5)Hint 1 Hint 2 Hint 3 Hint 4AB^+CD^+EF^+IH^\widehat{AB}+\widehat{CD}+\widehat{EF}+\widehat{IH}AB+CD+EF+IH=2π⋅2(60360+60360+120360+120360)=2\pi\cdot2\left(\frac{60}{360}+\frac{60}{360}+\frac{120}{360}+\frac{120}{360}\right)=2π⋅2(36060+36060+360120+360120)=4π=4\pi=4πHint 5AI=BC=DE=GF=GH=4AI=BC=DE=GF=GH=4AI=BC=DE=GF=GH=4Final Answer(C) 4π+204\pi+204π+20
