AMC 8 2026 (Problem 23)Plane GeometryHardLakshmi 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 TopicsCoreCircle TangencyMinorArea FormulasCheck AnswerYour answer:ABCDECheckHints (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+20Related Problems (10)AMC 10A 2025 (Problem 10)AMC 12A 2025 (Problem 24)AMC 10B 2025 (Problem 12)AMC 10B 2025 (Problem 20)AIME II 2026 (Problem 10)2024 AMC 10A Problem 14AMC 10B 2024 (Problem 21)AIME I 2025 (Problem 6)AMC 10A 2025 (Problem 22)AIME I 2026 (Problem 3)View all related problems →
