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A brand new triangle centre?

Locate the point \(\text{O}\) in a \(\Delta \text{ABC}\) such that for points \(\text{L, M}\) and \(\text{N}\) on sides \(\text{BC, CA}\) and \(\text{AB}\) respectively such that \(\Delta \text{LOC, } \Delta \text{MOA}\) and \(\Delta \text{NOB}\) have the same area and \(\text{LO}||\text{AC}, \text{MO}||\text{AB}\) and \(\text{NO}||\text{BC}\).


  • This is a proof problem, so you must give a proof

Note by Sharky Kesa
1 year, 8 months ago

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And prove that such a point is unique! Xuming Liang · 1 year, 8 months ago

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@Xuming Liang Did you get it? Sharky Kesa · 1 year, 8 months ago

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@Sharky Kesa yes...can I post it? Xuming Liang · 1 year, 8 months ago

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@Xuming Liang Sure, but if you want, post it privately on Slack. Let's have it up for a week, before the answer. Sharky Kesa · 1 year, 8 months ago

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