MathDB

G3

Part of 2022 Azerbaijan JBMO TST

Problems(1)

Triangles, orthocenter and reflection, proving AF intersects middle point BC

Source: Azerbaijan 2022 JBMO TST G3.

7/5/2022
In acute, scalene Triangle ABCABC, HH is orthocenter,BD BD and CECE are heights. X,YX,Y are reflection of AA from DD,EE respectively such that the pointsX,Y X,Y are on segments DCDC and EBEB. The intersection of circles HXY HXY and ADEADE is F.F. ( F≠HF \neq H). Prove thatAF AF intersects middle point of BCBC. ( MM in the diagram is Midpoint of BCBC)
geometrygeometric transformationreflection