Tuesday, November 22nd

Problem
Let ABCD be a square and F be a point on BC; draw the perpendicular to DF through B and let it cut DC at Q. Find the angle FQC.

Solution
Let P be intersection BQ with DF. Since the quadrilaterals CQPF and CDBQ are both cyclic, we have that the angles FQC, FPC and DBC are equal we have that FQC is 45.