Suppose $P$ is any point within an acute-angled triangle,Let $X,Y,Z$ be the feet of the perpendiculars from $P$ onto the sides $BC,CA,AB$ respectively. and $U,V,W$ be where $AP,BP,CP$ meet the sides $BC,AC,AB$ respectively.
show that：
$$|UV|+|UW|+|VW|\ge |XY|+|XZ|+|YZ|$$
This problem is from New Zealand 2015 TST exam ,It is said no one solved it in the olympiad. Everyone got 0 point.Background Pedal Triangle http://mathworld.wolfram.com/PedalTriangle.html
