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Omni-MATH / Let ABC be a triangle with AB=2,CA=3,BC=4. Let D be the point diametrically opposite A on the circumcircle of ABC, and let E lie on line AD such that D is the midpoint of (AE)¯. Li…

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problem

Let ABCA B C be a triangle with AB=2,CA=3,BC=4A B=2, C A=3, B C=4. Let DD be the point diametrically opposite AA on the circumcircle of ABCA B C, and let EE lie on line ADA D such that DD is the midpoint of AE¯\overline{A E}. Line ll passes through EE perpendicular to AE¯\overline{A E}, and FF and GG are the intersections of the extensions of AB¯\overline{A B} and AC¯\overline{A C} with ll. Compute FGF G.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=2,CA=3,BC=4. Let D be the point diametrically opposite A on the circumcircle of ABC, and let E lie on line AD such that D is the midpoint of (AE)¯. Line l passes through E perpendicular to (AE)¯, and F and G are the intersections of the extensions of (AB)¯ and (AC)¯ with l. Compute FG.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=2, C A=3, B C=4$. Let $D$ be the point diametrically opposite $A$ on the circumcircle of $A B C$, and let $E$ lie on line $A D$ such that $D$ is the midpoint of $\overline{A E}$. Line $l$ passes through $E$ perpendicular to $\overline{A E}$, and $F$ and $G$ are the intersections of the extensions of $\overline{A B}$ and $\overline{A C}$ with $l$. Compute $F G$.

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Source and history

task_id
5c0f882b-227a-5721-99d5-74875e81c558
task_key
test--5c0f882b-227a-5721-99d5-74875e81c558
task_revision_id
1
config / split
/ test

Official source

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