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Omni-MATH / 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…

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problem

Fix a triangle ABCABC. We say that triangle XYZXYZ is elegant if XX lies on segment BCBC, YY lies on segment CACA, ZZ lies on segment ABAB, and XYZXYZ is similar to ABCABC (i.e., ∠A=∠X,∠B=∠Y,∠C=∠Z\angle A=\angle X, \angle B=\angle Y, \angle C=\angle Z ). Of all the elegant triangles, which one has the smallest perimeter?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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., $\angle A=\angle X, \angle B=\angle Y, \angle C=\angle Z $). Of all the elegant triangles, which one has the smallest perimeter?

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Source and history

task_id
005a532e-a316-557e-b440-c3d48aa7047e
task_key
test--005a532e-a316-557e-b440-c3d48aa7047e
task_revision_id
1
config / split
/ test

Official source

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