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

Asked by gspublicschool | 8th Sep, 2018, 06:04: AM

Expert Answer:

 
 
If point O is in the quadrilateral, then join O to A, B , C and D
 
Now in triangle OAB
 
OA+OB>AB ... since sum of two sides is always greater than third
 
now if we add any term on left hand side the term will be even more greater
 
so, OA+OB+OC+OD>AB.
 
Similarly look in the triangle OBC,
OB+OC>BC
 
now add OA and OD on left hand side
 
so, OA+OB+OC+OD>BC

Answered by Sneha shidid | 12th Sep, 2018, 11:33: AM