Δευτέρα, 25 Μαρτίου 2013

RADICAL CENTERS, CIRCUMCIRCLE, EXCIRCLES

Let ABC be a triangle and Ia,Ib,Ic the excenters and O the circumcenter.

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

Δεν υπάρχουν σχόλια:

Δημοσίευση σχολίου

 

Free Hit Counter