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Omni-MATH / Let ABC be a triangle with AB=5, BC=6, and AC=7. Let its orthocenter be H and the feet of the altitudes from A,B,C to the opposite sides be D,E,F respectively. Let the line DF inte…

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problem

Let ABCABC be a triangle with AB=5AB=5, BC=6BC=6, and AC=7AC=7. Let its orthocenter be HH and the feet of the altitudes from A,B,CA, B, C to the opposite sides be D,E,FD, E, F respectively. Let the line DFDF intersect the circumcircle of AHFAHF again at XX. Find the length of EXEX.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=5, BC=6, and AC=7. Let its orthocenter be H and the feet of the altitudes from A,B,C to the opposite sides be D,E,F respectively. Let the line DF intersect the circumcircle of AHF again at X. Find the length of EX.
Original LaTeX notation
Let $ABC$ be a triangle with $AB=5$, $BC=6$, and $AC=7$. Let its orthocenter be $H$ and the feet of the altitudes from $A, B, C$ to the opposite sides be $D, E, F$ respectively. Let the line $DF$ intersect the circumcircle of $AHF$ again at $X$. Find the length of $EX$.

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Source and history

task_id
16f4640c-0010-5bad-b036-ca9f6ee6dbef
task_key
test--16f4640c-0010-5bad-b036-ca9f6ee6dbef
task_revision_id
1
config / split
/ test

Official source

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