Question

If 0 is a point within a quadrilateral ABCD, show that
OA+OB+OC + OD > AC + BD.​

Answer 1

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

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ANSWER

Given:- ABCD is a quadrilateral. O is a point inside the quadrilateral ABCD.

To prove:- OA+OB+OC+OD>AC+BD

Construction : Join OA,OB,OC and OD. Also, join AC and BD.

Proof:- As we know that the sum of any two sides of a triangle is greater than the third side.

Therefore,

In △BOD,

OB+OD>BD.....(1)

Similarly

In △AOC,

OA+OC>AC.....(2)

Adding eq

n

(1)&(2), we have

OB+OD+OA+OC>BD+AC

∴OA+OB+OC+OD>AC+BD

Hence proved.