Drepte concurente in triunghi

[Mateescu Constantin]

Fie \( \triangle ABC \) si \( P \) un punct interior acestuia. Notam \( AP\cap BC=\{D\},\ BP\cap AC=\{E\},\ CP\cap AB=\{F\} \) si \( DE\cap CF=\{U},\ EF\cap AD=\{V\},\ FD\cap BE=\{W\} \).

Fie \( \{A_1\}=AW\cap BC,\ \{A_2\}=AU\cap BC,\ \{B_1\}=BU\cap AC,\ \{B_2\}=BV\cap AC,\ \{C_1\}=CV\cap AB,\ \{C_2\}=CW\cap AB. \)

Demonstrati ca dreptele \( A_1B_2,\ B_1C_2,\ C_1A_2 \) sunt concurente in \( P \).