There are some special points in any triangle, as [Fermat point](https://en.wikipedia.org/wiki/Fermat_point), [symmedian point](https://en.wikipedia.org/wiki/Symmedian#Symmedian_point), [incenter](https://en.wikipedia.org/wiki/Incenter), [Morley center](https://en.wikipedia.org/wiki/Morley_centers), et cetera.

>>Let $P$ be a point on the plane, $PA$, $PB$, $PC$ meet $BC$, $CA$, $AB$ at $A'$, $B'$, $C'$ respectively. From my construction by [geogebra sofware](https://en.wikipedia.org/wiki/GeoGebra). I proposed a conjecture: 

   >>*In any triangle exist two points $P$ so that: $AA'=BB'=CC'$.*

>>**My question:** Is the conjecture above correct?

[![enter image description here][1]][1]

**My geogebra:**

The Red locus: If $P$ lie on red locus then $AA'=CC'$.

The Blue locus: If $P$ lie on red locus then $AA'=BB'$.

The Pink locus: If $P$ lie on pink locus then $CC'=BB'$

**See also:**

- [Triangle centers](http://faculty.evansville.edu/ck6/tcenters/index.html)


  [1]: https://i.sstatic.net/0sEAP.png