[alogo] Rotating a triangle in its circumcircle

Let A'B'C' be similar to the triangle ABC and rotating on a circle "d" concentric to the circumcircle "c" of the triangle ABC. Join A with A', B with B' etc. Build the triangle of intersections A''B''C'' of the lines AA', BB' and CC'.
a) Show that the triangles A''B''C'' are similar to the tangential triangle A*B*C* of ABC.
b) Show that the locus of the circumcenters of A''B''C'' is a circle, independent of d.

Generalize for polygons inscribed in circles.
For a related subject look at the file : RotatingTriangle.html .

[0_0] [0_1] [0_2]
[1_0] [1_1] [1_2]
[2_0] [2_1] [2_2]

Produced with EucliDraw©