MathDB

Problem 5

Part of 2001 Mongolian Mathematical Olympiad

Problems(2)

similar to Pascal's Theorem

Source: Mongolia MO 2001 Grade 10 P5

4/12/2021
Let A,B,C,D,E,FA,B,C,D,E,F be the midpoints of consecutive sides of a hexagon with parallel opposite sides. Prove that the points AB∩DEAB\cap DE, BC∩EFBC\cap EF, AC∩DFAC\cap DF lie on a line.
geometryhexagonprojective geometry
geometry config in a circle

Source: Mongolia MO 2001 Teachers P5

4/12/2021
Chords ACAC and BDBD of a circle ww intersect at EE. A circle that is internally tangent to ww at a point FF also touches the segments DEDE and ECEC. Prove that the bisector of ∠AFB\angle AFB passes through the incenter of △AEB\triangle AEB.
geometry