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Diagonals of a Parallelogram

ABCD is a par...

Question

ABCD is a parallelogram with AC and BD as diagonals, intersecting each other at O. If AO = 2 cm and BO = 3cm, then

A

AC + BD = 8 cm

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B

AC + BD = 10 cm

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C

AC + BD = 12 cm

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Solution

The correct option is B AC + BD = 10 cm
We know that the diagonals of a parallelogram bisect each other.
So, AC bisects BD and BD bisects AC.
Given, AO $= 2 c m$ . Hence AC $= 4 c m$
Also, BO $= 3 c m$ and hence BD $= 6 c m$
Therefore,
AC + BD $= 4 c m + 6 c m = 10 c m$

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