IMO 2022 Shortlist G5
Let ABC be a triangle, and let 1 and 2 be two parallel lines. For i “ 1,2, let i meet the lines BC, CA, and AB at Xi, Yi...
Category: Geometry
Problem
Let ABC be a triangle, and let 1 and 2 be two parallel lines. For i “ 1,2, let `i
meet the lines BC, CA, and AB at Xi, Yi, and Zi, respectively. Suppose that the line through
Xi perpendicular to BC, the line through Yi perpendicular to CA, and finally the line through
Zi perpendicular to AB, determine a non-degenerate triangle ∆i.
Show that the circumcircles of ∆1 and ∆2 are tangent to each other.
(Vietnam)