MathDB

2018.11.4.1

Part of Kyiv City MO Seniors 2003+ geometry

Problems(1)

orthocenter AXY lies on BD, <ADC =< ACB (2018 Kyiv City MO 11.4.1 )

Source:

9/12/2020
In the quadrilateral ABCDABCD, the diagonal ACAC is the bisector ∠BAD\angle BAD and ∠ADC=∠ACB\angle ADC = \angle ACB. The points X,  YX, \, \, Y are the feet of the perpendiculars drawn from the point AA on the lines BC,  CDBC, \, \, CD, respectively. Prove that the orthocenter ΔAXY\Delta AXY lies on the line BDBD.
orthocentergeometryequal angles