Fix a triangle ABC. We say that triangle XYZ is elegant if X lies on segment BC, Y lies on segment CA, Z lies on segment AB, and XYZ is similar to ABC (i.e., ∠A=∠X,∠B=∠Y,∠C=∠Z). Of all the elegant triangles, which one has the smallest perimeter? geometryinequalitiesoptimizationgeometric inequalitykomal