A perspector in Conway configuration
- Dear all
I suppose this is already known.
Let ABC be a triangle.Consider the Conway configuration(configuration of
Conway circle)i.e On sides AB and AC,past A,consider points P1 and P2
respectively such that AP1 = AP2.Similarly construct points P3,P4(on BC and
AC respectively) and P5 and P6(on AB and BC respectively).
Let P12 = P1P3/\P2P6 and P45 = P3P5/\P4P6
(P12 , P45 are on the either sides of A)
Similarly P56 = P1P5/\P4P6 and P23 = P1P3/\P2P4
and P34 = P2P4/\P3P5 and P16 = P2P6/\P1P5
Then line P12P45 passes through A and similarly lines P56P23 passes
through B and line P34P16 passes through C.
Thus triangles P12P34P56 and P45P23P16 are perspective with ABC at
I suppose there are many more things to investigate in this
Happy new year
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