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Question

In the picture below, if the diagonals of the square ABCD intersects at O, then .


A
AB2 = OB2
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B
AB2 < DC2
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C
AO2= CO2
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Solution

The correct option is C AO2= CO2

Construction: Join PQ, where P and Q are midpoints of AD and BC.
We have, AB||PQ||DC.



We know that,
Three or more parallel lines cut any two lines in the same ratio.

Therefore,
AOCO =BODO
AO × DO = BO × CO

Since ABCD is a square,
AO = DO = BO = CO
Hence, AO × AO = CO × CO

AO2= CO2


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