ZA-SAMO 1995 Problem 2

$ABC$ is a triangle with $\hat{A}<\hat{C}$ , and $D$ is the point on $BC$ such that $B\hat{A}D=A\hat{C}B$ . The perpendicular bisectors of $AD$ and $AC$ intersect in the point $E$ . Prove that $B\hat{A}E=90^\circ$ .