Question 55
Suppose that $A$-excircle of triangle $ABC$ is tangent to $AC$ and $AB$ at $E$ and $F$, respectively. Denote by $I_a$ the center of preceding circle. Point $D$ is the reflection of $A$ around the line $I_aB$. Lines $DI_a$ and $EF$ meet at $K$. Prove that the circumcenter of $DKE$, midpoint of $BC$ and $I_a$ are collinear.