MathDB

8.5

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

are all segments equal if alll circumradii are equal?

Source: 2021 Sharygin Geometry Olympiad Finals grade VIII p5

8/2/2021
Points A1,A2,A3,A4A_1,A_2,A_3,A_4 are not concyclic, the same for points B1,B2,B3,B4B_1,B_2,B_3,B_4. For all i,j,ki, j, k the circumradii of triangles AiAjAkA_iA_jA_k and BiBjBkB_iB_jB_k are equal. Can we assert that AiAj=BiBjA_iA_j=B_iB_j for all i,ji, j'?
geometryequal circlescircumradiusequal segments