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Omni-MATH / Let ABC be a triangle such that AB=13,BC=14,CA=15 and let E,F be the feet of the altitudes from B and C, respectively. Let the circumcircle of triangle AEF be ω. We draw three line…

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problem

Let ABCA B C be a triangle such that AB=13,BC=14,CA=15A B=13, B C=14, C A=15 and let E,FE, F be the feet of the altitudes from BB and CC, respectively. Let the circumcircle of triangle AEFA E F be ω\omega. We draw three lines, tangent to the circumcircle of triangle AEFA E F at A,EA, E, and FF. Compute the area of the triangle these three lines determine.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle such that AB=13,BC=14,CA=15 and let E,F be the feet of the altitudes from B and C, respectively. Let the circumcircle of triangle AEF be ω. We draw three lines, tangent to the circumcircle of triangle AEF at A,E, and F. Compute the area of the triangle these three lines determine.
Original LaTeX notation
Let $A B C$ be a triangle such that $A B=13, B C=14, C A=15$ and let $E, F$ be the feet of the altitudes from $B$ and $C$, respectively. Let the circumcircle of triangle $A E F$ be $\omega$. We draw three lines, tangent to the circumcircle of triangle $A E F$ at $A, E$, and $F$. Compute the area of the triangle these three lines determine.

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Source and history

task_id
bcf27bd8-9059-56fa-820a-b873beb435d5
task_key
test--bcf27bd8-9059-56fa-820a-b873beb435d5
task_revision_id
1
config / split
/ test

Official source

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