Solution: Two line segments AB and CD of length m and n intersect each other at point O.
Considering it is a two dimensional plane and O being the origin, and AB being X axis and CD being Y axis.
Coordinates of A=(m/2,0), Coordinate of B=(-m/2,0)
Coordinate of C=(0,n/2), Coordinate of D=(0,-n/2)
Let P(m/2, n/2) be any point in that plane.
OA+OB+OC+OD=m/2+m/2+n/2+n/2=m+n----------------(1)
PA+PB+PC+PD= n/2+[tex]\sqrt{m^{2}+\frac{n^{2} }{4}[/tex]+m/2+[tex]\sqrt{{n^{2} +\frac{m^{2}}{4}}[/tex]
As, [tex]\sqrt{m^{2}+\frac{n^{2} }{4}[/tex] is always greater than m and [tex]\sqrt{{n^{2} +\frac{m^{2}}{4}}[/tex] is always greater than n .
So,PA+PB+PC+PD will always be>m+n. ----------(2)
Combining (1) and (2), we arrived at the result
PA+PB+PC+PD>OA+OB+OC+OD
