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Omni-MATH / A convex hexagon ABCDEF is inscribed in a circle. Prove the inequality AC⋅BD⋅CE⋅DF⋅AE⋅BF≥27AB⋅BC⋅CD⋅DE⋅EF⋅FA.

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problem

A convex hexagon ABCDEFA B C D E F is inscribed in a circle. Prove the inequality AC⋅BD⋅CE⋅DF⋅AE⋅BF≥27AB⋅BC⋅CD⋅DE⋅EF⋅FAA C \cdot B D \cdot C E \cdot D F \cdot A E \cdot B F \geq 27 A B \cdot B C \cdot C D \cdot D E \cdot E F \cdot F A.
Plain-text mathematical notation (without MathML)
A convex hexagon ABCDEF is inscribed in a circle. Prove the inequality AC⋅BD⋅CE⋅DF⋅AE⋅BF≥27AB⋅BC⋅CD⋅DE⋅EF⋅FA.
Original LaTeX notation
A convex hexagon $A B C D E F$ is inscribed in a circle. Prove the inequality $A C \cdot B D \cdot C E \cdot D F \cdot A E \cdot B F \geq 27 A B \cdot B C \cdot C D \cdot D E \cdot E F \cdot F A$.

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Source and history

task_id
0719c868-35a3-51b0-83ef-a63400f8a338
task_key
test--0719c868-35a3-51b0-83ef-a63400f8a338
task_revision_id
1
config / split
/ test

Official source

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