MathDB

2

Part of 2001 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

equal segments given and wanted, circumcenters, symmetric point, perpendicular,

Source: Rioplatense Olympiad 2001 level 3 P2

9/5/2018
Let ABCABC be an acute triangle and A1,B1A_1, B_1 and C1C_1, points on the sides BC,CABC, CA and ABAB, respectively, such that CB1=A1B1CB_1 = A_1B_1 and BC1=A1C1BC_1 = A_1C_1. Let DD be the symmetric of A1A_1 with respect to B1C1,OB_1C_1, O and O1O_1 are the circumcenters of triangles ABCABC and A1B1C1A_1B_1C_1, respectively. If A≠D,O≠O1A \ne D, O \ne O_1 and ADAD is perpendicular to OO1OO_1, prove that AB=ACAB = AC.
geometryequal segmentsCircumcentersymmetryperpendicular