Question 12
The $ABCD$ trapezium of bases $AB$ and $CD$, and non-parallel sides $BC$ and $DA$, has $\angle A=90^\circ$, $AB=6$, $CD=3$ and $AD=4$. Let $E$, $G$, $H$ be the circumcenters of the triangles $ABC$, $ACD$, $ABD$, respectively. Find the area of triangle $EGH$.
**CLARIFICATION:** The circumcenter of a triangle is the point of intersection of the three bisectors of its sides.
**CLARIFICATION:** The circumcenter of a triangle is the point of intersection of the three bisectors of its sides.