MathDB
XN // BC wanted, angle bisector, midpoint, circle (AB)

Source: Netherlands - Dutch NMO 2023 p4

March 25, 2024
parallelgeometryangle bisector

Problem Statement

In acute-angled triangle ABCABC with ∣BC∣<∣BA∣|BC| < |BA|, point NN is the midpoint of ACAC. The circle with diameter ABAB intersects the bisector of ∠B\angle B in two points: BB and XX. Prove that XNXN is parallel to BCBC. https://cdn.artofproblemsolving.com/attachments/5/1/f0ae8f5df8f2cc1bb80de1ee1807dc845a87b3.png
Back to ProblemsView on AoPS