MathDB
Equal segments in a circumscribed quadrilateral

Source: Baltic Way 2018, Problem 14

November 6, 2018
geometry

Problem Statement

A quadrilateral ABCDABCD is circumscribed about a circle ω\omega. The intersection point of ω\omega and the diagonal ACAC, closest to AA, is EE. The point FF is diametrally opposite to the point EE on the circle ω\omega. The tangent to ω\omega at the point FF intersects lines ABAB and BCBC in points A1A_1 and C1C_1, and lines ADAD and CDCD in points A2A_2 and C2C_2, respectively. Prove that A1C1=A2C2A_1C_1=A_2C_2.
Back to ProblemsView on AoPS