MathDB
perpendicularity for Czech, Polish and Slovak juniors

Source: Czech-Polish-Slovak Junior Match 2018, individual p5 CPSJ

February 1, 2020
geometryperpendicularcircumcirclearc midpointSymmetric

Problem Statement

An acute triangle ABCABC is given in which AB<ACAB <AC. Point EE lies on the ACAC side of the triangle, with AB=AEAB = AE. The segment ADAD is the diameter of the circumcircle of the triangle ABCABC, and point SS is the center of this arc BCBC of this circle to which point AA does not belong. Point FF is symmetric of point DD wrt SS. Prove that lines FEF E and ACAC are perpendicular.
Back to ProblemsView on AoPS