IR-TST 2008 Problem 12

In the acute-angled triangle $ABC$ , $D$ is the intersection of the altitude passing through $A$ with $BC$ and $I_a$ is the excenter of the triangle with respect to $A$ . $K$ is a point on the extension of $AB$ from $B$ , for which $\angle AKI_a=90^\circ+\frac 34\angle C$ . $I_aK$ intersects the extension of $AD$ at $L$ . Prove that $DI_a$ bisects the angle $\angle AI_aB$ iff $AL=2R$ . ( $R$ is the circumradius of $ABC$ )