AMC 10A 2025 (Problem 10)A semicircle has diameter AB‾\overline{AB}AB and chord CD‾\overline{CD}CD of length 161616 parallel to AB‾\overline{AB}AB. A smaller semicircle with diameter on AB‾\overline{AB}AB and tangent to CD‾\overline{CD}CD is cut from the larger semicircle, as shown below. What is the area of the resulting figure, shown shaded?(A) 16π\text{(A)}\;16\pi(A)16π(B) 24π\text{(B)}\;24\pi(B)24π(C) 32π\text{(C)}\;32\pi(C)32π(D) 48π\text{(D)}\;48\pi(D)48π(E) 64π\text{(E)}\;64\pi(E)64πRelated TopicsCoreToolkit 68 — Circles, Tangents, and Radical AxisMajorToolkit 54 — Area Formulas and Important Geometry FormulasHints (3)Hint 1Hint 2R2=r2+82R^2=r^2+8^2R2=r2+82⟹R2−r2=64\Longrightarrow R^2-r^2=64⟹R2−r2=64Hint 3Areashaded=12π(R2−r2)=32π\text{Area}_{\text{shaded}}=\frac12\pi(R^2-r^2)=32\piAreashaded=21π(R2−r2)=32πFinal Answer(C) 32π32\pi32πRelated Problems (7)AMC 10A/12A 2023 (Problem 18/22)AMC 8 2026 (Problem 23)AIME I 2025 (Problem 6)MathCounts 2026 Chapter Sprint Round (Problem 28)AMC 10B/12B 2024 (Problem 14/9)AMC 12A 2024 (Problem 20)MATHCOUNTS State Team 2025 (Problem 9)
