MathDB
2019 All Russian MO Grade 9 P3

Source:

May 1, 2019
geometrycircumcircle

Problem Statement

Circle Ω\Omega with center OO is the circumcircle of an acute triangle △ABC\triangle ABC with AB<BCAB<BC and orthocenter HH. On the line BOBO there is point DD such that OO is between BB and DD and ∠ADC=∠ABC\angle ADC= \angle ABC . The semi-line starting at HH and parallel to BOBO wich intersects segment ACAC , intersects Ω\Omega at EE. Prove that BH=DEBH=DE.
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