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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
2 years, 1 month ago

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And prove that such a point is unique!

- 2 years, 1 month ago

Did you get it?

- 2 years, 1 month ago

yes...can I post it?

- 2 years, 1 month ago

Sure, but if you want, post it privately on Slack. Let's have it up for a week, before the answer.

- 2 years, 1 month ago