MathDB
concurrent wanted, midpoints and angle bisectors related

Source: 2021 Sharygin Finals grades X-XI p2

August 1, 2021
geometryangle bisectormidpointconcurrentconcurrency

Problem Statement

Let ABCABC be a scalene triangle, and AoA_o, Bo,B_o, CoC_o be the midpoints of BCBC, CACA, ABAB respectively. The bisector of angle CC meets AoCoA_oCo and BoCoB_oC_o at points B1B_1 and A1A_1 respectively. Prove that the lines AB1AB_1, BA1BA_1 and AoBoA_oB_o concur.