Tuesday, December 22, 2020

1614. Geometric Mean Perspector

3 comments:

  1. Nice problem.
    * You can consider intersection points both in the positive part and negative part and you get two perspectors P1 and P2.
    * The line P1P2 goes through X(n) for n=1, 57, 1360, 1699, 1709, 1768, 1836, 3358, 4312, 5805, 7956, 7965, 8727, 11219, 11246, 11372, 13226, 15299, 17728, 24465
    * The circle through the circumcenter O and also through P1, P2 goes through X(7330).

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  2. ABC is orthologic to A1B1C1 and A2B2C2. In both case orthology center is X(1)-incenter of ABC.

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  3. X(1)X(3) line of ABC is Euler Line of A1B1C! and A2B2C2.

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