Question 2
Rectangles $BCC_1B_2$, $CAA_1C_2$, and $ABB_1A_2$ are erected outside an acute triangle $ABC$. Suppose
$$\angle BC_1C+\angle CA_1A+\angle AB_1B=180^\circ.$$
Prove that $B_1C_2$, $C_1A_2$, and $A_1B_2$ are concurrent.
Proposed by Ankan Bhattacharya. Evan Chen’s third-party solution notes: https://aops.com/community/p21498558; source video https://youtu.be/9WNgDETHOlI?t=890. One point is nonofficial editorial normalization; manual essay grading only.
$$\angle BC_1C+\angle CA_1A+\angle AB_1B=180^\circ.$$
Prove that $B_1C_2$, $C_1A_2$, and $A_1B_2$ are concurrent.
Proposed by Ankan Bhattacharya. Evan Chen’s third-party solution notes: https://aops.com/community/p21498558; source video https://youtu.be/9WNgDETHOlI?t=890. One point is nonofficial editorial normalization; manual essay grading only.