MathDB

8.2

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

prove A1B1C1 and A2B2C2 are similar

Source: Sharygin Finals 2023 8.2

8/2/2023
The bisectors of angles AA, BB, and CC of triangle ABCABC meet for the second time its circumcircle at points A1A_1, B1B_1, C1C_1 respectively. Let A2A_2, B2B_2, C2C_2 be the midpoints of segments AA1AA_1, BB1BB_1, CC1CC_1 respectively. Prove that the triangles A1B1C1A_1B_1C_1 and A2B2C2A_2B_2C_2 are similar.
geometrySharygin Geometry OlympiadSharygin 2023similar triangles