Given two circles a, b, intersecting at D and F. Consider point C moving on b. Show that the chord AB has constant length. Show that the projection G, of A on BC describes a circle tangent to b.
Show that, as C moves on circle b, then for the triangle ABC:
1) Its centroid describes a circle.
2) Its circucenter describes a circle concentric with circle a.
3) The intersection-point of ÁÅ, ÂD describes a circle, passing through D and E.
4) The orthocenter describes a circle concentric with circle b.
![[alogo]](alogo.png){kind=small}
A problem on inscribed angles ![[0_0]](Constant_Length_Chord_files/Constant_Length_Chord_0_0_0.png)
![[0_1]](Constant_Length_Chord_files/Constant_Length_Chord_0_0_1.png)
![[1_0]](Constant_Length_Chord_files/Constant_Length_Chord_0_1_0.png)
![[1_1]](Constant_Length_Chord_files/Constant_Length_Chord_0_1_1.png)