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Omni-MATH / Let ABC be a triangle with AB=7,BC=9, and CA=4. Let D be the point such that AB‖CD and CA‖BD. Let R be a point within triangle BCD. Lines ℓ and m going through R are parallel to CA…

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problem

Let ABCA B C be a triangle with AB=7,BC=9A B=7, B C=9, and CA=4C A=4. Let DD be the point such that AB‖CDA B \| C D and CA‖BDC A \| B D. Let RR be a point within triangle BCDB C D. Lines ℓ\ell and mm going through RR are parallel to CAC A and ABA B respectively. Line ℓ\ell meets ABA B and BCB C at PP and $P^{\prime}$ respectively, and mm meets CAC A and BCB C at QQ and $Q^{\prime}$ respectively. If SS denotes the largest possible sum of the areas of triangles $B P P^{\prime}, R P^{\prime} Q^{\prime}$, and $C Q Q^{\prime}$, determine the value of S2S^{2}.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=7,BC=9, and CA=4. Let D be the point such that AB‖CD and CA‖BD. Let R be a point within triangle BCD. Lines ℓ and m going through R are parallel to CA and AB respectively. Line ℓ meets AB and BC at P and $P^{\prime}$ respectively, and m meets CA and BC at Q and $Q^{\prime}$ respectively. If S denotes the largest possible sum of the areas of triangles $B P P^{\prime}, R P^{\prime} Q^{\prime}$, and $C Q Q^{\prime}$, determine the value of S².
Original LaTeX notation
Let $A B C$ be a triangle with $A B=7, B C=9$, and $C A=4$. Let $D$ be the point such that $A B \| C D$ and $C A \| B D$. Let $R$ be a point within triangle $B C D$. Lines $\ell$ and $m$ going through $R$ are parallel to $C A$ and $A B$ respectively. Line $\ell$ meets $A B$ and $B C$ at $P$ and $P^{\prime}$ respectively, and $m$ meets $C A$ and $B C$ at $Q$ and $Q^{\prime}$ respectively. If $S$ denotes the largest possible sum of the areas of triangles $B P P^{\prime}, R P^{\prime} Q^{\prime}$, and $C Q Q^{\prime}$, determine the value of $S^{2}$.

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Source and history

task_id
9c0ca4d6-012e-58d5-901f-5b2b0a91d95f
task_key
test--9c0ca4d6-012e-58d5-901f-5b2b0a91d95f
task_revision_id
1
config / split
/ test

Official source

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