Notes
two triangles and a quarter circle solution

Solution to the Two Triangles and a Quarter Circle Puzzle

Solution by Angle in a Semi-Circle

In the above diagram, the original two triangles are reflected in the horizontal edge of the quarter-circle, and the quarter-circle is completed to a full circle.

As the green triangles are congruent, $D C A$ is a straight line. Therefore, angle $A \hat{D} B$ is the angle in a semi-circle so is $90^\circ$.