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Omni-MATH / Let ABC be a triangle with AB=13,BC=14,CA=15. The altitude from A intersects BC at D. Let ω₁ and ω₂ be the incircles of ABD and ACD, and let the common external tangent of ω₁ and …

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problem

Let ABCA B C be a triangle with AB=13,BC=14,CA=15A B=13, B C=14, C A=15. The altitude from AA intersects BCB C at DD. Let ω1\omega_{1} and ω2\omega_{2} be the incircles of ABDA B D and ACDA C D, and let the common external tangent of ω1\omega_{1} and ω2\omega_{2} (other than BCB C) intersect ADA D at EE. Compute the length of AEA E.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=13,BC=14,CA=15. The altitude from A intersects BC at D. Let ω₁ and ω₂ be the incircles of ABD and ACD, and let the common external tangent of ω₁ and ω₂ (other than BC) intersect AD at E. Compute the length of AE.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=13, B C=14, C A=15$. The altitude from $A$ intersects $B C$ at $D$. Let $\omega_{1}$ and $\omega_{2}$ be the incircles of $A B D$ and $A C D$, and let the common external tangent of $\omega_{1}$ and $\omega_{2}$ (other than $B C$) intersect $A D$ at $E$. Compute the length of $A E$.

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task_id
d5dd4c18-88da-5828-8874-16438e355849
task_key
test--d5dd4c18-88da-5828-8874-16438e355849
task_revision_id
1
config / split
/ test

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