09/07/19 22:55:17
>>199
△ABC の3辺の長さを
AB = x+y, BC = y+z, CA = z+x,
とおき >>163 を使うと
AI = √{x(x+y)(x+z)/s} = bcR,
BI = √{y(y+z)(y+x)/s} = caR,
CI = √{z(z+x)(z+y)/s} = abR,
2r = 2√(xyz/s) = abcR,
R = (y+z)(z+x)(x+y)/{4√(xyzs)},
s = x+y+z,
∴ (AI+BI+CI-2r)/R = bc + ca + ab -abc,