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Omni-MATH / Let ABC be a triangle with AB=5,BC=8,CA=11. The incircle ω and A-excircle ^{1} Gamma are centered at I₁ and I₂, respectively, and are tangent to BC at D₁ and D₂, respectively. Find…

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problem

Let ABCA B C be a triangle with AB=5,BC=8,CA=11A B=5, B C=8, C A=11. The incircle ω\omega and AA-excircle $^{1} \Gamma$ are centered at I1I_{1} and I2I_{2}, respectively, and are tangent to BCB C at D1D_{1} and D2D_{2}, respectively. Find the ratio of the area of △AI1D1\triangle A I_{1} D_{1} to the area of △AI2D2\triangle A I_{2} D_{2}.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=5,BC=8,CA=11. The incircle ω and A-excircle $^{1} \Gamma$ are centered at I₁ and I₂, respectively, and are tangent to BC at D₁ and D₂, respectively. Find the ratio of the area of △AI₁D₁ to the area of △AI₂D₂.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=5, B C=8, C A=11$. The incircle $\omega$ and $A$-excircle $^{1} \Gamma$ are centered at $I_{1}$ and $I_{2}$, respectively, and are tangent to $B C$ at $D_{1}$ and $D_{2}$, respectively. Find the ratio of the area of $\triangle A I_{1} D_{1}$ to the area of $\triangle A I_{2} D_{2}$.

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Source and history

task_id
dbec0694-9839-5c66-85f8-a747519ff69f
task_key
test--dbec0694-9839-5c66-85f8-a747519ff69f
task_revision_id
1
config / split
/ test

Official source

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