## Two perspective triangles, developpment to new centers?

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• Dear Hyacinthists, 1. ABC a triangle, 2. A’B’C’ the médial triangle of ABC 3. M and N two antigonal points wrt ABC 4. PQR the homothetic triangle of
Message 1 of 2 , Aug 30, 2011
Dear Hyacinthists,
1. ABC a triangle,
2. A’B’C’ the médial triangle of ABC
3. M and N two antigonal points wrt ABC
4. PQR the homothetic triangle of A’B’C’ with centre N and ratio 2
5. A”B”C” the antipedal triangle of ABC wrt M (PA perpendicular to B”C” and so on)
More generally, we can consider the anti isogonic triangle so that <PAB” and so on are all egal…
Conclusion : A”B”C” and PQR are perspective.
Application to pair of antigonal points centers?
Sincerely
Jean-Louis

[Non-text portions of this message have been removed]
• Dear Hyacinthists, 1. ABC a triangle, 2. A’B’C’ the médial triangle of ABC 3. M and N two antigonal points wrt ABC 4. PQR the homothetic triangle of
Message 2 of 2 , Aug 30, 2011
Dear Hyacinthists,
1. ABC a triangle,
2. A’B’C’ the médial triangle of ABC
3. M and N two antigonal points wrt ABC
4. PQR the homothetic triangle of A’B’C’ with centre N and ratio 2
5. A”B”C” the antipedal triangle of ABC wrt M (PA perpendicular to B”C” and so on)
More generally, we can consider the anti isogonic triangle so that <PAB” and so on are all egal…
Conclusion : A”B”C” and PQR are perspective.
Application to pair of antigonal points centers?
Sincerely
Jean-Louis

[Non-text portions of this message have been removed]
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