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## Locus

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• Let ABC be a triangle, and PaPbPc the pedal triangle of P. The line IPa intersects the circumcircle of ABC at A1,A2 The line IPb intersects the circumcircle of
Message 1 of 235 , Jan 1, 1970
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Let ABC be a triangle, and PaPbPc the pedal triangle of P.

The line IPa intersects the circumcircle of ABC at A1,A2
The line IPb intersects the circumcircle of ABC at B1,B2
The line IPc intersects the circumcircle of ABC at C1,C2
(where A1,B1,C1 lie on the positive side of the corresponding
triangle sides, and A2,B2,C2 on the negative side).

Which is the locus of P such that the triangles
ABC, A1B1C1; ABC, A2B2C2 are perspective?

In general: Instead of the incenter I, a fixed point Q = (f:g:h).

Antreas

PS: Sorry if this isn't "The first time that Antreas asked this
question,"
• Let ABC be a triangle and P a point Which is the locus of P such that PA + PB + PC = 0 (signed segments) ? APH PS see special case
Message 235 of 235 , Apr 10
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Let ABC be a triangle and P a point

Which is the locus ofÂ  P such that PA + PB + PC = 0
(signed segments) ?

APH

PS see special case

https://www.facebook.com/photo.php?fbid=811391552270276&set=p.811391552270276&type=1&theater
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