Question 34
Point $D$ lies on the side $[BC]$ of $\triangle ABC$. The circumcenters of $\triangle ADC$ and $\triangle BAD$ are $O_{1}$ and $O_{2}$, respectively, and $O_{1}O_{2} \parallel AB$. The orthocenter of $\triangle ADC$ is $H$ and $AH = O_{1}O_{2}$. Find the angles of $\triangle ABC$ if $2m(\angle C) = 3m(\angle B)$.