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In the Parallelogram $ABCD, {AD}^{2} - {AB}^{2} =$

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4 $AB$ . (projection of $AD$ on $AB$ )

$AC$ . (projection of $BD$ on $AC$ )

2 $AC$ . (projection of $BD$ on $AC$ )

2 $AB$ . (projection of $AD$ on $AB$ )

answer is C.

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Detailed Solution

${AD}^{2} - {AB}^{2} = b^{2} - a^{2} = (b + a) . (b - a) AC = a + b BD = b - a proj BD on AC = \frac{BD . AC}{|AC|} ∴ BD . AC = |AC| (proj BD on AC)$ Question Image

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