There are some special points in any triangle. A special point in a triangle as Fermat point, symmedian point, incenter, Morley center, et setera....
Let $P$ be a point on the plane, $PA$, $PB$, $PC$ meets $BC$, $CA$, $AB$ at $A'$, $B'$, $C'$. From my construction by geogebra sofware. I proposed a conjecture: In any triangle exist two points $P$ so that: $AA'=BB'=CC'$.
My question: Is the conjecture above correct?
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: