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Omni-MATH / Triangle ABC is given with AB=13,BC=14,CA=15. Let E and F be the feet of the altitudes from B and C, respectively. Let G be the foot of the altitude from A in triangle AFE. Find AG…

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problem

Triangle ABCA B C is given with AB=13,BC=14,CA=15A B=13, B C=14, C A=15. Let EE and FF be the feet of the altitudes from BB and CC, respectively. Let GG be the foot of the altitude from AA in triangle AFEA F E. Find AGA G.
Plain-text mathematical notation (without MathML)
Triangle ABC is given with AB=13,BC=14,CA=15. Let E and F be the feet of the altitudes from B and C, respectively. Let G be the foot of the altitude from A in triangle AFE. Find AG.
Original LaTeX notation
Triangle $A B C$ is given with $A B=13, B C=14, C A=15$. Let $E$ and $F$ be the feet of the altitudes from $B$ and $C$, respectively. Let $G$ be the foot of the altitude from $A$ in triangle $A F E$. Find $A G$.

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