Question 10
G4 (GBR). For a triangle $T=ABC$ we take the point $X$ on the side $(AB)$ such that $AX/XB=4/5$, the point $Y$ on the segment $(CX)$ such that $CY=2YX$, and, if possible, the point $Z$ on the ray $(CA$ such that $\angle CXZ=180^\circ-\angle ABC$. We denote by $\Sigma$ the set of all triangles $T$ for which $\angle XYZ=45^\circ$.
Prove that all the triangles from $\Sigma$ are similar and find the measure of their smallest angle.
Prove that all the triangles from $\Sigma$ are similar and find the measure of their smallest angle.