MathDB
Finding two circumcenters

Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P3 day 1

November 10, 2024
geometrycircumcircle

Problem Statement

Let ABCABC a triangle with circumcircle Γ\Gamma and circumcenter OO. A point XX, different from AA, BB, CC, or their diametrically opposite points, on Γ\Gamma, is chosen. Let ω\omega the circumcircle of COXCOX. Let EE the second intersection of XAXA with ω\omega, FF the second intersection of XBXB with ω\omega and DD a point on line ABAB such that CD⊥EFCD \perp EF. Prove that EE is the circumcenter of ADCADC and FF is the circumcenter of BDCBDC.
Back to ProblemsView on AoPS