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Omni-MATH / Equilateral triangle ABC has circumcircle Ω. Points D and E are chosen on minor arcs AB and AC of Ω respectively such that BC=DE. Given that triangle ABE has area 3 and triangle …

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problem

Equilateral triangle ABCABC has circumcircle Ω\Omega. Points DD and EE are chosen on minor arcs ABAB and ACAC of Ω\Omega respectively such that BC=DEBC=DE. Given that triangle ABEABE has area 3 and triangle ACDACD has area 4, find the area of triangle ABCABC.
Plain-text mathematical notation (without MathML)
Equilateral triangle ABC has circumcircle Ω. Points D and E are chosen on minor arcs AB and AC of Ω respectively such that BC=DE. Given that triangle ABE has area 3 and triangle ACD has area 4, find the area of triangle ABC.
Original LaTeX notation
Equilateral triangle $ABC$ has circumcircle $\Omega$. Points $D$ and $E$ are chosen on minor arcs $AB$ and $AC$ of $\Omega$ respectively such that $BC=DE$. Given that triangle $ABE$ has area 3 and triangle $ACD$ has area 4, find the area of triangle $ABC$.

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Source and history

task_id
843cf626-321e-5143-be5b-50ce17e3782f
task_key
test--843cf626-321e-5143-be5b-50ce17e3782f
task_revision_id
1
config / split
/ test

Official source

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