Question

If O is a point within a quadrilateral ABCD show that OA+OB+OC+OD>AC+BD

Answer 1

Let ABCD BE A QUADRILATERAL WHOSE DIAGONALS ARE AC AND BD ABD O ANY POINT WITHIN QUADRILATERAL .



JOIN O WITH A,B,C,D

IN ACO

OA+OC > A.C. ...... ( 1 )
( IN triangle sum of 2 SIDESGREATER than 3rd sides )

similarly in BOD

OB+OD > BD......... (2)

ADDING BOTH EQUATION WE GET

OA+OC +OB+OD> AC+ BD .

.