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Omni-MATH / Let ABC be a triangle with AB=AC=(25)/(14)BC. Let M denote the midpoint of (BC)¯ and let X and Y denote the projections of M onto (AB)¯ and (AC)¯, respectively. If the areas of tri…

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problem

Let ABCA B C be a triangle with AB=AC=2514BCA B=A C=\frac{25}{14} B C. Let MM denote the midpoint of BC¯\overline{B C} and let XX and YY denote the projections of MM onto AB¯\overline{A B} and AC¯\overline{A C}, respectively. If the areas of triangle ABCA B C and quadrilateral AXMYA X M Y are both positive integers, find the minimum possible sum of these areas.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=AC=(25)/(14)BC. Let M denote the midpoint of (BC)¯ and let X and Y denote the projections of M onto (AB)¯ and (AC)¯, respectively. If the areas of triangle ABC and quadrilateral AXMY are both positive integers, find the minimum possible sum of these areas.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=A C=\frac{25}{14} B C$. Let $M$ denote the midpoint of $\overline{B C}$ and let $X$ and $Y$ denote the projections of $M$ onto $\overline{A B}$ and $\overline{A C}$, respectively. If the areas of triangle $A B C$ and quadrilateral $A X M Y$ are both positive integers, find the minimum possible sum of these areas.

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Source and history

task_id
e8916c16-8cd3-546f-8dff-920306c178d6
task_key
test--e8916c16-8cd3-546f-8dff-920306c178d6
task_revision_id
1
config / split
/ test

Official source

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