Question 3
Let $ABC$ be a triangle with $BC=a,CA=b,AB=c$ and $a\ne b\ne c$. In its plane choose $A',B',C'$ so that:
1. The pairs $A,A'$; $B,B'$; $C,C'$ are either all on the same side, or all on opposite sides, of $BC,CA,AB$, respectively.
2. The triangles $A'BC,B'CA,C'AB$ are similar isosceles triangles.
Determine $\angle A'BC$ in terms of $a,b,c$ so that the lengths $AA',BB',CC'$ are not the side lengths of a triangle. A triangle is understood in the ordinary nondegenerate sense: its three vertices are not collinear.
1. The pairs $A,A'$; $B,B'$; $C,C'$ are either all on the same side, or all on opposite sides, of $BC,CA,AB$, respectively.
2. The triangles $A'BC,B'CA,C'AB$ are similar isosceles triangles.
Determine $\angle A'BC$ in terms of $a,b,c$ so that the lengths $AA',BB',CC'$ are not the side lengths of a triangle. A triangle is understood in the ordinary nondegenerate sense: its three vertices are not collinear.