{"schema":"vela.problem-packet.v0.1","problem":898,"statement":"If $A,B,C\\in \\mathbb{R}^2$ form a triangle and $P$ is a point in the interior then, if $N$ is where the perpendicular from $P$ to $AB$ meets the triangle, and similarly for $M$ and $L$,\\[\\overline{PA}+\\overline{PB}+\\overline{PC}\\geq 2(\\overline{PM}+\\overline{PN}+\\overline{PL}).\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}