Is the centroid of $ABCD$ the arithmetic centroid ( $\frac{1}{4}(A+B+C+D)$) or the lamina centroid (center of mass of an $ABCD$-shaped piece of uniform material)

center of mass it means

edit: nvm

keratinwarrior wrote: Is the centroid of $ABCD$ the arithmetic centroid ( $\frac{1}{4}(A+B+C+D)$) or the lamina centroid (center of mass of an $ABCD$-shaped piece of uniform material) They are equivalent. Whenever the term centroid appers in a math olympiad problem, I'd say it's safe to assume it always refers to the arithmetic centroid.