19/10/20 19:36:54.69 KcpV49eI.net
>>810
A(1,0,0)
B(x=cosθ,sinθ,0)
C(cosθ,-sinθ,0)
0<θ<π
O(k,0,h)
AO=(k-1,0,h)
BO=(k-cosθ,-sinθ,h)
CO=(k-cosθ,sinθ,h)
AO・BO=AO・CO=(k-1)(k-cosθ)+h^2=0
BO・CO=(k-cosθ)^2-sin^2θ+h^2=0
(cosθ-1)(k-cosθ)+sin^2θ=0
k=cosθ+sin^2θ/(1-cosθ)=1+2cosθ
h^2=sin^2θ-(1+cosθ)^2=-2cosθ-2cos^2θ=-2x^2-2x=-2x(x+1)≦1/2
0<h≦1/√2