Notes
two squares on a triangle solution

Solution to the Two Squares on a Triangle Puzzle

Solution by Angle in a Semi-Circle, Angle at the Circumference is Half the Angle at the Centre

With the points labelled as above, point $O$ is the midpoint of $B D$ so the circle centred on $O$ which passes through $B$ also passes through $A$ and $D$. Since the angle in a semi-circle is $90^\circ$ and angle $D \hat{C} B$ is $90^\circ$, the circle also passes through $C$. Then angle $A \hat{O} B$ is $90^\circ$ so since the angle at the circumference is half the angle at the centre, angle $A \hat{C} B$ is $45^\circ$.