  We study the dual of Philo's shortest line segment problem which asks to find
the optimal line segments passing through two given points, with a common
endpoint, and with the other endpoints on a given line. The provided solution
uses multivariable calculus and geometry methods. Interesting connections with
the angle bisector of the triangle are explored. A generalization of the
problem using $L_p$ ($p\ge 1$) norm is proposed. Particular case $p=\infty$ is
studied. Interesting case $p=2$ is proposed as an open problem and related
property of a symedian of a triangle is conjectured.
