Selection Examination for Juniors

A triangle $AB\Gamma$ is given with $\hat{A}=105°$ and $\hat{\Gamma }=\frac{\hat{B}}{4}$.

α. Determine the measures of the angles $\hat{B}$ and $\hat{\Gamma }$.

β. If $O$ is the center of the circumcircle of the triangle $AB\Gamma$ and $\Delta$ is the antipodal of $B$, prove that the distance of $\Gamma$ from $B\Delta$ is $\frac{B\Delta }{4}$.