MathDB

G5

Part of 2022 IMO Shortlist

Problems(1)

What happened to geometry

Source: 2022 G5

7/9/2023
Let ABCABC be a triangle and ℓ1,ℓ2\ell_1,\ell_2 be two parallel lines. Let ℓi\ell_i intersects line BC,CA,ABBC,CA,AB at Xi,Yi,ZiX_i,Y_i,Z_i, respectively. Let Δi\Delta_i be the triangle formed by the line passed through XiX_i and perpendicular to BCBC, the line passed through YiY_i and perpendicular to CACA, and the line passed through ZiZ_i and perpendicular to ABAB. Prove that the circumcircles of Δ1\Delta_1 and Δ2\Delta_2 are tangent.
geometryIMO ShortlistISL 2022