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Omni-MATH / Let XYZ be an equilateral triangle, and let K,L,M be points on sides XY,YZ,ZX, respectively, such that XK/KY=B,YL/LZ=1/C, and ZM/MX=1. Determine the ratio of the area of triangle …

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problem

Let XYZX Y Z be an equilateral triangle, and let K,L,MK, L, M be points on sides XY,YZ,ZXX Y, Y Z, Z X, respectively, such that XK/KY=B,YL/LZ=1/CX K / K Y=B, Y L / L Z=1 / C, and ZM/MX=1Z M / M X=1. Determine the ratio of the area of triangle KLMK L M to the area of triangle XYZX Y Z.
Plain-text mathematical notation (without MathML)
Let XYZ be an equilateral triangle, and let K,L,M be points on sides XY,YZ,ZX, respectively, such that XK/KY=B,YL/LZ=1/C, and ZM/MX=1. Determine the ratio of the area of triangle KLM to the area of triangle XYZ.
Original LaTeX notation
Let $X Y Z$ be an equilateral triangle, and let $K, L, M$ be points on sides $X Y, Y Z, Z X$, respectively, such that $X K / K Y=B, Y L / L Z=1 / C$, and $Z M / M X=1$. Determine the ratio of the area of triangle $K L M$ to the area of triangle $X Y Z$.

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Source and history

task_id
7f1e869a-7cf4-525b-bc78-70cb99722350
task_key
test--7f1e869a-7cf4-525b-bc78-70cb99722350
task_revision_id
1
config / split
/ test

Official source

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