MathDB
BC bisects <FBG, if BD = CD and EF //CD

Source: 2021 All-Ukrainain Correspondence MO , grades 5-12 p11

June 24, 2022
geometryangle bisectorUkraine Correspondence

Problem Statement

Let DD be a point on the side ABAB of the triangle ABCABC such that BD=CDBD = CD, and let the points EE on the side BCBC and FF on the extension ACAC beyond the point CC be such that EF∥CDEF\parallel CD. The lines AEAE and CDCD intersect at the point GG. Prove that BCBC is the bisector of the angle FBGFBG.
Back to ProblemsView on AoPS