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

Posted by Sahil Singh 8 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Naveen Sharma 8 years, 10 months ago

Ans.

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.

\(In \triangle BOD, \)

OB + OD > BD …........(1)

Similarly \(In \triangle AOC, \)

OA + OC > AC ….........(2)

Adding (1) and (2), we obtain

OB + OD + OA + OC > BD + AC

Therefore; OA + OB + OC + OD > AC + BD

Hence Proved

0Thank You

ANSWER

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