SMO 2006 Open Round 1 Question 13

In triangle $ABC$, $\angle A=20^\circ$, $\angle C=90^\circ$, $O$ is a point on $AB$, and $D$ is the midpoint of $OB$. Suppose the circle centred at $O$ with radius $OD$ touches the side $AC$ at $T$. Determine $\angle BCD$ in degrees.