- APHR. G. SANGER: SYNTHETIC PROJECTIVE GEOMETRY (1939)For a proof I offer the book:[APH]:Anopolis #850

In fact we can take any point P (instead of H) and any points

O1,O2,O3 on the circumcircles of PBC,PCA,PAB, resp.

Then the circumcircles of the triangles

AO2O3, BO3O1, CO1O2

are concurrent.

http://groups.yahoo.com/neo/groups/Anopolis/conversations/messages/850

- It sounds old! And for a reference the offer holds as well !!.the circumcircles of AB'C', BC'A', CA'B' are also concurrent .If the circumcircles of A'BC, B'CA, C'AB are concurrent, thenThe problem is equivalent to this:Let ABC, A'B'C' be two triangles.Note: From the other version ie"If P is a fixed point and O1,O2,O3 three variable points onthe circumcircles of PBC,PCA,PAB, resp then the circumcirclesof AO2O3, BO3O1, CO1O2 are concurrent" we may ask:As O1,O2,O3 move on the respective circles, in what plane regionthe points of concurrence are located on?(I think it is not the entire plane)

APHOn Sat, Sep 14, 2013 at 1:04 PM, Antreas Hatzipolakis <anopolis72@...> wrote:[Attachment(s) from Antreas Hatzipolakis included below]APHR. G. SANGER: SYNTHETIC PROJECTIVE GEOMETRY (1939)For a proof I offer the book:[APH]:Anopolis #850

In fact we can take any point P (instead of H) and any points

O1,O2,O3 on the circumcircles of PBC,PCA,PAB, resp.

Then the circumcircles of the triangles

AO2O3, BO3O1, CO1O2

are concurrent.

http://groups.yahoo.com/neo/groups/Anopolis/conversations/messages/850

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