X(502)={(b + c) (-a^3 - a^2 (b + c) + (b - c) (b + c)^2 + a (b^2 - b c - c^2)) (a^3 + a^2 (b + c) + (b - c) (b + c)^2 + a (b^2 + b c - c^2)), (a + c) (a^3 + a^2 (b + c) + (b - c) (b + c)^2 + a (b^2 + b c - c^2)) (a^3 - b^3 - b^2 c - b c^2 - c^3 + a^2 (b + c) - a (b^2 + b c + c^2)), (a + b) (a^3 + a^2 (b + c) - (b - c) (b + c)^2 + a (-b^2 + b c + c^2)) (a^3 - b^3 - b^2 c - b c^2 - c^3 + a^2 (b + c) - a (b^2 + b c + c^2))}
The circle (NaNbNc) which is centered at X(5), has radius
ReplyDeletesquared R^2/4 - (abc s r)/(2S^2), and passes through X(k), k ∈ {10, 502, 946}.
Elias M. Hagos
X(502)={(b + c) (-a^3 - a^2 (b + c) + (b - c) (b + c)^2 +
ReplyDeletea (b^2 - b c - c^2)) (a^3 + a^2 (b + c) + (b - c) (b + c)^2 +
a (b^2 + b c - c^2)), (a + c) (a^3 +
a^2 (b + c) + (b - c) (b + c)^2 + a (b^2 + b c - c^2)) (a^3 -
b^3 - b^2 c - b c^2 - c^3 + a^2 (b + c) -
a (b^2 + b c + c^2)), (a + b) (a^3 +
a^2 (b + c) - (b - c) (b + c)^2 + a (-b^2 + b c + c^2)) (a^3 -
b^3 - b^2 c - b c^2 - c^3 + a^2 (b + c) - a (b^2 + b c + c^2))}