Question 34
Trapezoid $ABCD$, with $AB \parallel CD$, has side lengths $AB = 11$, $BC = 8$, $CD = 19$, and $DA = 4$. Compute the area of the convex quadrilateral whose vertices are the circumcenters of $\triangle ABC$, $\triangle BCD$, $\triangle CDA$, and $\triangle DAB$.