Diagonals AC and BD of a parallelogram ABCD intersect each other at O.If OA = 3 cm and OD = 2 cm, determine the length of AC.

2.0 cm

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4.0 cm

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3.6 cm

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6.0 cm

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Solution

The correct option is B 6.0 cm
$A B C D i s a p a r a l l e l o g r a m . ∴ A B ∥ D C ⟹ ∠ A B D = ∠ B D C & ∠ A C D = ∠ B A C (a l t ∠^{s}) A l s o A B = D C (o p p o s i t e s i d e s o f a p a r a l l e l o g r a m) ∴ Δ A O B & Δ D O C a r e c o n g r u e n t b y A S A t e s t . ∴ A O = O C = 3 c m & D O = O B = 2 c m . N o w A C = A O + O C = (3 + 3) c m = 6 c m a n d B D = D O + O B = (2 + 2) c m = 4 c m . T h e r e f o r e - A C = 6 c m, B D = 4 c m$

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