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

#Geometry #Proofs #Sharky

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

And prove that such a point is unique!

Xuming Liang - 5 years, 9 months ago

Did you get it?

Sharky Kesa - 5 years, 9 months ago

yes...can I post it?

Xuming Liang - 5 years, 9 months ago

@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 - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$