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AIME 2025 I / On △ABC points A,D,E, and B lie that order on side…

Problem

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question

On △ABC\triangle ABC points A,D,EA,D,E, and BB lie that order on side AB¯\overline{AB} with AD=4,DE=16AD=4, DE=16, and EB=8EB=8. Points A,F,GA,F,G, and CC lie in that order on side AC¯\overline{AC} with AF=13,FG=52AF=13, FG=52, and GC=26GC=26. Let MM be the reflection of DD through FF, and let NN be the reflection of GG through EE. Quadrilateral DEGFDEGF has area 288. Find the area of heptagon AFNBCEMAFNBCEM.
Plain-text mathematical notation (without MathML)
On △ABC points A,D,E, and B lie that order on side (AB)¯ with AD=4,DE=16, and EB=8. Points A,F,G, and C lie in that order on side (AC)¯ with AF=13,FG=52, and GC=26. Let M be the reflection of D through F, and let N be the reflection of G through E. Quadrilateral DEGF has area 288. Find the area of heptagon AFNBCEM.
Original LaTeX notation
On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.

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Source and history

task_id
ae2cd3e6-5b7c-55aa-9abf-c3869c959937
task_key
AIME2025~2dI--test--ae2cd3e6-5b7c-55aa-9abf-c3869c959937
task_revision_id
3
config / split
AIME2025-I / test

Official source

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