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Omni-MATH / Let ABP,BCQ,CAR be three non-overlapping triangles erected outside of acute triangle ABC. Let M be the midpoint of segment AP. Given that …
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problem
Let be three non-overlapping triangles erected outside of acute triangle . Let be the midpoint of segment . Given that
$ \angle PAB \equal{} \angle CQB \equal{} 45^\circ$, $ \angle ABP \equal{} \angle QBC \equal{} 75^\circ$, $ \angle RAC \equal{} 105^\circ$, and $ RQ^2 \equal{} 6CM^2$, compute .
[i]Zuming Feng.[/i]Plain-text mathematical notation (without MathML)
Let ABP,BCQ,CAR be three non-overlapping triangles erected outside of acute triangle ABC. Let M be the midpoint of segment AP. Given that $ \angle PAB \equal{} \angle CQB \equal{} 45^\circ$, $ \angle ABP \equal{} \angle QBC \equal{} 75^\circ$, $ \angle RAC \equal{} 105^\circ$, and $ RQ^2 \equal{} 6CM^2$, compute AC²/AR².
[i]Zuming Feng.[/i]Original LaTeX notation
Let $ ABP, BCQ, CAR$ be three non-overlapping triangles erected outside of acute triangle $ ABC$. Let $ M$ be the midpoint of segment $ AP$. Given that $ \angle PAB \equal{} \angle CQB \equal{} 45^\circ$, $ \angle ABP \equal{} \angle QBC \equal{} 75^\circ$, $ \angle RAC \equal{} 105^\circ$, and $ RQ^2 \equal{} 6CM^2$, compute $ AC^2/AR^2$.
[i]Zuming Feng.[/i]Discussion
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