1969 AMC 12 Question 30
AMC12 · 1969 AMC 12
Let $P$ be a point of hypotenuse $AB$ (or its extension) of isosceles right triangle $ABC.$ Let $s=AP^2+PB^2.$ Then:
$s\lt2CP^2$ for a finite number of positions of $P$
$s\lt2CP^2$ for an infinite number of positions of $P$
$s=2CP^2$ only if $P$ is the midpoint of $AB$ or an
endpoint of $AB$
$s=2CP^2$ always
$s\gt2CP^2$ if $P$ is a trisection point of $AB$