TCS: P6 - P10

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• [Hatzipolakis - F. Javier] Let ABC be a triangle, P = (x:y:z) a point and A B C the pedal triangle of P. Denote: A* := (The Reflection of BC in BP) / (The
Message 1 of 1 , Jul 25, 2013
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[Hatzipolakis - F. Javier]

Let ABC be a triangle, P = (x:y:z) a point and A'B'C'
the pedal triangle of P.

Denote:

A* := (The Reflection of BC in BP) /\ (The Reflection of BC in CP)

B* := (The Reflection of CA in CP) /\ (The Reflection of CA in AP)

C* := (The Reflection of AB in AP) /\ (The Reflection of AB in BP)

[The triangles A*BC, B*CA, C*AB share the same incenter P]

Oa := The Circumcenter of A*BC
Ob := The Circumcenter of B*CA
Oc := The Circumcenter of C*AB

P* := The Point of Concurrence of the Circumcircles
of A*BC, B*CA, C*AB
[We have seen recently this point in Hyacinthos]

La := The Reflection of P*Oa in B'C'

Lb := The Reflection of P*Ob in C'A'

Lc := The Reflection of P*Oc in A'B'.

The Triangles ABC, Triangle bounded by (La,Lb,Lc)
are parallelogic for P on the Euler line.

One of the parallelocic centers lies on the circumcircle.

Coordinates of Parallelogic centers on the circumcircle
for P = H, O, G, N and midpointGH in a File in the Reference:

http://tech.groups.yahoo.com/group/Anopolis/message/126
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