r945

Let P, Q be two points. Define A1 = APÇBQ, A2 = APÇCQ, B1 = BPÇCQ, B2 = BPÇAQ, C1 = CPÇAQ,  C2 = CPÇBQ. Then the triangles ABC, A1B1C1, A2B2C2 are triply perspective:
{ABC}, {C1A1B1} center Q {ABC}, {A1B1C1} center P
{ABC}, {B2C2A2} center Q  {ABC}, {A2B2C2} center P
{A1B1C1}, {C2A2B2} center Q {A1B1C1}, {A2B2C2} center P

The other three centers
{ABC}, {B1C1A1} center X {ABC}, {C2A2B2} center Y {A1B1C1}, {B2C2A2} center Z
are collinear.
The six axis of the perspectives centered at P or Q concur at a point T, tripole of the line PQ, and the three axis of the perspectives centered at X, Y, Z coincide in a line t.
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