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Question

Diagonal AC and BD of quadrilateral ABCD intersects each other at point O.

Prove that AB + BC + CD + AD  <  2 (AC + BD).  


Solution

In a quadrilateral ABCD, with diagonals intersecting at O. AO+OB>AB(INEQUALITY)

OD+OA>AD

OD+OC>DC

OB+OC>BC

ADDING

AO + OB + OA + OD + OC + OB + OC >  AB + AC + BC + CD

(AC+BD+AC+BD)>AB+BC+CD+AD

2(AC+BD)>AB+AC+BC+CD

HENCE YES THE STATEMENT IS TRUE


Mathematics

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