Question

ABCD is a quadilateral, there is a point o inside it. Prove that AO+BO+CO+DO>AC+BD​

Answer 1

Step-by-step explanation:

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

RTP: OA + OB + OC + OD > AC + BD

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

Proof : The sum of any two sides of a triangle is always greater than the third side.

In ΔBOD, OB + OD > BD …........(1)

Similarly In ΔAOC, OA + OC > AC ….........(2)

Adding equations (1) and (2), we will get OB + OD + OA + OC > BD + AC

∴ OA + OB + OC + OD > AC + BD