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bDistance
Ivan Pavlov edited this page May 2, 2022
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1 revision
bDistance[p,q]
Gives the distance between p, q, which are defined in barycentrics. For example, let's calculate the distance between circumcenter and incenter:
OI = bDistance[KimberlingCenterB[1], KimberlingCenterB[3]] // Simplify
SymmetricReduction[a^3 - a^2 (b + c) + (b - c)^2 (b + c) - a (b^2 - 3 b c + c^2), {a, b, c}]
{9 a b c + (a + b + c)^3 - 4 (a + b + c) (a b + a c + b c), 0}
SymmetricReduction[a^4 + (b^2 - c^2)^2 - 2 a^2 (b^2 + c^2), {a, b, c}]
{8 a b c (a + b + c) + (a + b + c)^4 - 4 (a + b + c)^2 (a b + a c + b c), 0}
Hence: