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in Mathematics by (80.8k points)

In rhombus ABCD,

AB2 + BC2 + CD2 + DA2 =

(A) OA2 + OB2

(B) OB2 + OC2

(C) OC2 + OD2

(D) AC2 + BD2

1 Answer

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Best answer

The correct option is: (D) AC2 + BD2

Explanation:

Let the length of sides of rhombus be x, length of OC be x1 and length of OD be y1. Then AB2 + BC2 + CD2 + DA2 = 4x2 

Since, AC and DB bisect each other at O.

. .. AC = 2x1 and BD = 2y1 

ln ΔAOD, ΔDOC, ΔAOB, ΔBOC

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