[alogo] A problem on inscribed angles

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.

[0_0] [0_1]
[1_0] [1_1]


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 , D describes a circle, passing through D and E.
4) The orthocenter describes a circle concentric with circle b.


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