MathDB

2019.10.5

Part of Kharkiv City MO Seniors - geometry

Problems(1)

K is the orthocenter of II_aE, excenter (Kharkiv City X 2019 Ukr)

Source:

3/22/2020
In triangle ABCABC, pointI I is incenter , IaI_a is the AA-excenter. Let KK be the intersection point of the BCBC with the external bisector of the angle BACBAC, and EE be the midpoint of the arc BACBAC of the circumcircle of triangle ABCABC. Prove that KK is the orthocenter of triangle IIaEII_aE.
geometryexcenterincenterangle bisectormidpointKharkiv