Question

ABCD is a square. Diagonals AC and BD intersect each other at O. Bisector of∠BAC meet BO at P and BC at Q. Prove that OP = ½ CQ

Answer 1

O is the mid point of AC (since the diagonals of square bisect each other)

And, P is the mid point of AQ by converse of mid point theorem

But, OP||CQ & OP=1/2CQ (By mid point theorem)