Found problems: 1
2020 DMO Stage 1, 5.
[b]Q.[/b] Let $ABC$ be a triangle, where $L_A, L_B, L_C$ denote the internal angle bisectors of $\angle BAC, \angle ABC, \angle ACB$ respectively and $\ell_A, \ell_B, \ell_C$, the altitudes from the corresponding vertices. Suppose $ L_A\cap \overline{BC} = \{A_1\}$, $\ell_A \cap \overline{BC} = \{A_2\}$ and the circumcircle of $\triangle AA_1A_2$ meets $AB$ and $AC$ at $S$ and $T$ respectively. If $\overline{ST} \cap \overline{BC} = \{A'\}$, prove that $A',B',C'$ are collinear, where $B'$ and $C'$ are defined in a similar manner.
[i]Proposed by Functional_equation[/i]