Question

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

Answer 1

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Raghunath , SubjectMatterExpert

Member since Apr 11 2014

Sol:

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 :  By triangle in equality the sum of any two sides of a triangle is greater than the third side.

In ΔBOD,

OB + OD > BD …........(1)

Similarly

In ΔAOC,

OA + OC > AC ….........(2)

Adding (1) and (2), we obtain

OB + OD + OA + OC > BD + AC

∴ OA + OB + OC + OD > AC + BD

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