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Omni-MATH / Let △ABC be an acute triangle, with M being the midpoint of (BC)¯, such that AM=BC. Let D and E be the intersection of the internal angle bisectors of ∠AMB and ∠AMC with AB and AC,…

Problem

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problem

Let △ABC\triangle A B C be an acute triangle, with MM being the midpoint of BC¯\overline{B C}, such that AM=BCA M=B C. Let DD and EE be the intersection of the internal angle bisectors of ∠AMB\angle A M B and ∠AMC\angle A M C with ABA B and ACA C, respectively. Find the ratio of the area of △DME\triangle D M E to the area of △ABC\triangle A B C.
Plain-text mathematical notation (without MathML)
Let △ABC be an acute triangle, with M being the midpoint of (BC)¯, such that AM=BC. Let D and E be the intersection of the internal angle bisectors of ∠AMB and ∠AMC with AB and AC, respectively. Find the ratio of the area of △DME to the area of △ABC.
Original LaTeX notation
Let $\triangle A B C$ be an acute triangle, with $M$ being the midpoint of $\overline{B C}$, such that $A M=B C$. Let $D$ and $E$ be the intersection of the internal angle bisectors of $\angle A M B$ and $\angle A M C$ with $A B$ and $A C$, respectively. Find the ratio of the area of $\triangle D M E$ to the area of $\triangle A B C$.

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Source and history

task_id
665c74b3-432d-579f-8d11-6650a0bc4a1b
task_key
test--665c74b3-432d-579f-8d11-6650a0bc4a1b
task_revision_id
1
config / split
/ test

Official source

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