[alogo] Triangle inscribed in triangle

The angles at O are equal : A'OA'' = B'OB'' = C'OC'' = w. Then the triangles A'B'C' and A''B''C'' are similar. OA', OB', OC' assumed to be orthogonal to the sides of ABC.
(Modify the red angle to turn A''B''C'' about O).

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All triangles A'B'C' similar to a fixed triangle t' inscribed in the triangle t(ABC), and having A' opposite to A, B' opposite to B, C' opposite to C result from A'B'C' by a "turn" as above. Notice that the angle(A'OB') = angle(A''OB'') = 2ð-angle(C), and correspondingly the other angles by which O is viewing the side of A''B''C'' are fixed. Thus, the relative position of O w.r. to t' is fixed.

Thus, considering the 6 different ways to pair opposite angles of the two triangles, we get 6 "inscription-centers" (or pivots) of triangle t' to t. Reversing the orientation of the triangle t' we get 6 more pivots.

Challenge: construct a User-Tool that selects two triangles t, t' and constructs the 12 "Inscription_Centers" of t' inscribed in t. For a picture of the 12 pivots look at SixPivots.html .

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