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