MathDB

2021.11

Part of Ukraine Correspondence MO - geometry

Problems(1)

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

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

6/24/2022
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.
geometryangle bisectorUkraine Correspondence