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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

\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

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

Official source

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