Question 186
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 $\frac{B\Delta}{4}$.
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 $\frac{B\Delta}{4}$.