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Omni-MATH / Let ABC be a triangle with AB=13,BC=14, and CA=15. We construct isosceles right triangle ACD with ∠ADC=90^(∘), where D,B are on the same side of line AC, and let lines AD and CB me…

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problem

Let ABCA B C be a triangle with AB=13,BC=14A B=13, B C=14, and CA=15C A=15. We construct isosceles right triangle ACDA C D with ∠ADC=90∘\angle A D C=90^{\circ}, where D,BD, B are on the same side of line ACA C, and let lines ADA D and CBC B meet at FF. Similarly, we construct isosceles right triangle BCEB C E with ∠BEC=90∘\angle B E C=90^{\circ}, where E,AE, A are on the same side of line BCB C, and let lines BEB E and CAC A meet at GG. Find cos∠AGF\cos \angle A G F.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=13,BC=14, and CA=15. We construct isosceles right triangle ACD with ∠ADC=90^(∘), where D,B are on the same side of line AC, and let lines AD and CB meet at F. Similarly, we construct isosceles right triangle BCE with ∠BEC=90^(∘), where E,A are on the same side of line BC, and let lines BE and CA meet at G. Find cos∠AGF.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=13, B C=14$, and $C A=15$. We construct isosceles right triangle $A C D$ with $\angle A D C=90^{\circ}$, where $D, B$ are on the same side of line $A C$, and let lines $A D$ and $C B$ meet at $F$. Similarly, we construct isosceles right triangle $B C E$ with $\angle B E C=90^{\circ}$, where $E, A$ are on the same side of line $B C$, and let lines $B E$ and $C A$ meet at $G$. Find $\cos \angle A G F$.

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task_id
e8196f81-ebda-5107-9d19-d9f5ef09793d
task_key
test--e8196f81-ebda-5107-9d19-d9f5ef09793d
task_revision_id
1
config / split
/ test

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