MathDB
concyclic points whose center lies on circumcircle wanted

Source: 2020 Dutch BxMO TST p2

November 21, 2020
geometryConcycliccyclic quadrilateral

Problem Statement

In an acute-angled triangle ABC,DABC, D is the foot of the altitude from AA. Let D1D_1 and D2D_2 be the symmetric points of DD wrt ABAB and ACAC, respectively. Let E1E_1 be the intersection of BCBC and the line through D1D_1 parallel to ABAB . Let E2E_2 be the intersection ofBC BC and the line through D2D_2 parallel to ACAC. Prove that D1,D2,E1D_1, D_2, E_1 and E2E_2 on one circle whose center lies on the circumscribed circle of △ABC\vartriangle ABC.
Back to ProblemsView on AoPS