IMO 2023 Shortlist G8
Let ABC be an equilateral triangle. Points A1, B1, C1 lie inside triangle ABC such that triangle A1B1C1 is scalene, BA1 ...
Category: Geometry
Problem
Let ABC be an equilateral triangle. Points A1, B1, C1 lie inside triangle ABC such
that triangle A1B1C1 is scalene, BA1 “ A1C, CB1 “ B1A, AC1 “ C1B and
=BA1C =CB1A =AC1B “ 480˝
.
Lines BC1 and CB1 intersect at A2; lines CA1 and AC1 intersect at B2; and lines AB1 and
BA1 intersect at C2.
Prove that the circumcircles of triangles AA1A2, BB1B2, CC1C2 have two common points.
(U.S.A.) Shortlisted problems 9