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Omni-MATH / Consider triangle ABC where BC=7,CA=8, and AB=9. D and E are the midpoints of BC and CA, respectively, and AD and BE meet at G. The reflection of G across D is G^{prime}, and …

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problem

Consider triangle ABCA B C where BC=7,CA=8B C=7, C A=8, and AB=9A B=9. DD and EE are the midpoints of BCB C and CAC A, respectively, and ADA D and BEB E meet at GG. The reflection of GG across DD is $G^{\prime}$, and $G^{\prime} E$ meets CGC G at PP. Find the length PGP G.
Plain-text mathematical notation (without MathML)
Consider triangle ABC where BC=7,CA=8, and AB=9. D and E are the midpoints of BC and CA, respectively, and AD and BE meet at G. The reflection of G across D is $G^{\prime}$, and $G^{\prime} E$ meets CG at P. Find the length PG.
Original LaTeX notation
Consider triangle $A B C$ where $B C=7, C A=8$, and $A B=9$. $D$ and $E$ are the midpoints of $B C$ and $C A$, respectively, and $A D$ and $B E$ meet at $G$. The reflection of $G$ across $D$ is $G^{\prime}$, and $G^{\prime} E$ meets $C G$ at $P$. Find the length $P G$.

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Source and history

task_id
8334a2bf-1dc2-547c-85da-87d735bfc41a
task_key
test--8334a2bf-1dc2-547c-85da-87d735bfc41a
task_revision_id
1
config / split
/ test

Official source

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