1.
Denote:
r1 = the rdical center of (O),(Ib),(Ic)
r2 = the rdical center of (O),(Ic),(Ia)
r3 = the rdical center of (O),(Ia),(Ib)
Perspective Triangles (?):
1.1. ABC, r1r2r3
1.2. IaIbIc, r1r2r3
2.
Denote:
Ja = the excenter of the excircle respective to BC of the triangle OBC
Jb = the excenter of the excircle respective to CA of the triangle OCA
Jc = the excenter of the excircle respective to AB of the triangle OAB
R1 = the rdical center of (O),(Jb),(Jc)
R2 = the rdical center of (O),(Jc),(Ja)
R3 = the rdical center of (O),(Ja),(Jb)
Perspective Triangles (?):
2.1. ABC, R1R2R3
2.2. JaJbJc, R1R2R3
3.
Denote:
i1 = the radical center of (Ja),(Ib),(Ic)
i2 = the radical center of (Jb),(Ic),(Ia)
i3 = the radical center of (Jc),(Ia),(Ib)
j1 = the radical center of (Ia),(Jb),(Jc)
j2 = the radical center of (Ib),(Jc),(Ja)
j3 = the radical center of (Ic),(Ja),(Jb)
Perspective triangles (?):
3.1. ABC, i1i2i3
3.2. ABC, j1j2j3
3.3. i1i2i3, j1j2j3
3.4. i1i2i3, IaIbIc
3.5. i1i2i3, JaJbJc
3.6. j1j2j3, IaIbIc
3.7. j1j2j3, JaJbJc
3.8. IaIbIc, JaJbJc
Antreas P. Hatzipolakis, 25 March 2013
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