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Omni-MATH / Let G₁G₂G₃ be a triangle with G₁G₂=7,G₂G₃=13, and G₃G₁=15. Let G₄ be a point outside triangle G₁G₂G₃ so that ray (G₁G₄)→ cuts through the interior of the triangle, G₃G₄=G₄G₂, and …

Problem

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problem

Let G1G2G3G_{1} G_{2} G_{3} be a triangle with G1G2=7,G2G3=13G_{1} G_{2}=7, G_{2} G_{3}=13, and G3G1=15G_{3} G_{1}=15. Let G4G_{4} be a point outside triangle G1G2G3G_{1} G_{2} G_{3} so that ray G1G4→\overrightarrow{G_{1} G_{4}} cuts through the interior of the triangle, G3G4=G4G2G_{3} G_{4}=G_{4} G_{2}, and ∠G3G1G4=30∘\angle G_{3} G_{1} G_{4}=30^{\circ}. Let G3G4G_{3} G_{4} and G1G2G_{1} G_{2} meet at G5G_{5}. Determine the length of segment G2G5G_{2} G_{5}.
Plain-text mathematical notation (without MathML)
Let G₁G₂G₃ be a triangle with G₁G₂=7,G₂G₃=13, and G₃G₁=15. Let G₄ be a point outside triangle G₁G₂G₃ so that ray (G₁G₄)→ cuts through the interior of the triangle, G₃G₄=G₄G₂, and ∠G₃G₁G₄=30^(∘). Let G₃G₄ and G₁G₂ meet at G₅. Determine the length of segment G₂G₅.
Original LaTeX notation
Let $G_{1} G_{2} G_{3}$ be a triangle with $G_{1} G_{2}=7, G_{2} G_{3}=13$, and $G_{3} G_{1}=15$. Let $G_{4}$ be a point outside triangle $G_{1} G_{2} G_{3}$ so that ray $\overrightarrow{G_{1} G_{4}}$ cuts through the interior of the triangle, $G_{3} G_{4}=G_{4} G_{2}$, and $\angle G_{3} G_{1} G_{4}=30^{\circ}$. Let $G_{3} G_{4}$ and $G_{1} G_{2}$ meet at $G_{5}$. Determine the length of segment $G_{2} G_{5}$.

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Source and history

task_id
525ca75a-ea09-5955-a9eb-2d3a088302c0
task_key
test--525ca75a-ea09-5955-a9eb-2d3a088302c0
task_revision_id
1
config / split
/ test

Official source

initial import