HYACINTHOS 10933

Dear friends,

I have found new points on the incircle

1.P1((b-c)^2/(s-a):(c-a)^2/(s-b):(a-b)^2/(s-c)).

2.P2((a(b-c))^2/(s-a):(b(c-a))^2/(s-b):((c(a-b))^2/(s-c)).

3.P3((b+c-2a)^2/(s-a):(c+a-2b)^2/(s-b):(a+b-2c)^2/(s-c)).

4.P4((b^2-c^2)^2/(s-a):(c^2-a^2)^2/(s-b):(a^2-b^2)^2/(s-c)).

5.P5((s-a)[2a^2-a(b+c)+(b-c)^2]:(s-b)[2b^2-b(c+a)+(c-a)^2]:
(s-c)[2c^2-c(a+b)+(a-b)^2])

This point is the antipode of Feuerbach point Fe=X(11)
X(11)=((b-c)^2(s-a):(c-a)^2(s-b):(a-b)^2(s-c))
on the Euler or nine-point circle.

6.P6(a^2(b-c)^2(s-a)^3:b^2(c-a)^2(s-b)^3:c^2(a-b)^2(s-c)^3).

Best regards

Milorad R.Stevanovic