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Omni-MATH / In acute △ABC with centroid G,AB=22 and AC=19. Let E and F be the feet of the altitudes from B and C to AC and AB respectively. Let G^{prime} be the reflection of G over BC. If …

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problem

In acute △ABC\triangle A B C with centroid G,AB=22G, A B=22 and AC=19A C=19. Let EE and FF be the feet of the altitudes from BB and CC to ACA C and ABA B respectively. Let $G^{\prime}$ be the reflection of GG over BCB C. If E,F,GE, F, G, and $G^{\prime}$ lie on a circle, compute BCB C.
Plain-text mathematical notation (without MathML)
In acute △ABC with centroid G,AB=22 and AC=19. Let E and F be the feet of the altitudes from B and C to AC and AB respectively. Let $G^{\prime}$ be the reflection of G over BC. If E,F,G, and $G^{\prime}$ lie on a circle, compute BC.
Original LaTeX notation
In acute $\triangle A B C$ with centroid $G, A B=22$ and $A C=19$. Let $E$ and $F$ be the feet of the altitudes from $B$ and $C$ to $A C$ and $A B$ respectively. Let $G^{\prime}$ be the reflection of $G$ over $B C$. If $E, F, G$, and $G^{\prime}$ lie on a circle, compute $B C$.

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Source and history

task_id
082abc76-9591-566a-8de9-418a20aed939
task_key
test--082abc76-9591-566a-8de9-418a20aed939
task_revision_id
1
config / split
/ test

Official source

initial import