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Question

In the given figure, ABCD is a rhombus. Then,
(a) AC2 + BD2 = AB2
(b) AC2 + BD2 = 2AB2
(c) AC2 + BD2 = 4AB2
(d) 2(AC2 + BD2) = 3AB2

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Solution

(c) ​AC2 + BD2 = 4AB2

Explanation:
We know that the diagonals of a rhombus bisect each other at right angles.
Here, OA = 12AC, OB = 12BD and ∠​AOB ​= 90°
Now, AB2= OA2 + OB2 = 14(AC)2 + 14(BD)2
∴ 4AB2 = (AC2 + BD2)

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