Question

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

• A. AO${}^2$= CO${}^2$
• B. AB${}^2$ < DC${}^2$
• C. AB${}^2$ = OB${}^2$

Answer 1

The correct option is A AO${}^2$= CO${}^2$

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,
$\frac{AO}{CO}$ =$\frac{BO}{DO}$
AO × DO = BO × CO

Since ABCD is a square,
AO = DO = BO = CO
Hence, AO × AO = CO × CO
AO${}^2$= CO${}^2$