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%I #5 Mar 30 2012 18:57:45
%S 1,6,4,4,5,0,8,0,6,0,3,2,3,0,2,4,2,4,9,0,0,0,2,9,9,7,3,1,4,3,0,5,1,3,
%T 3,1,4,8,7,5,9,6,6,3,2,9,1,3,1,4,2,8,2,3,4,6,5,7,9,9,0,2,4,0,2,4,4,3,
%U 1,7,7,8,7,2,2,0,2,2,3,8,3,8,8,5,5,0,3,6,2,6,4,9,3,8,6,0,2,8,5,1
%N Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(2,5,sqrt(29)).
%C See A195284 for definitions and a general discussion.
%e (A)=1.64450806032302424900029973143051331487596632913...
%t a = 2; b = 5; c = Sqrt[29]; f = 2 a*b/(a + b + c);
%t x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t x3 = f*Sqrt[2]
%t N[x1, 100]
%t RealDigits[%] (* (A) A195359 *)
%t N[x2, 100]
%t RealDigits[%] (* (B) A195360 *)
%t N[x3, 100]
%t RealDigits[%] (* (C) A195361 *)
%t N[(x1 + x2 + x3)/(a + b + c), 100]
%t RealDigits[%] (* Philo(ABC,I) A195362 *)
%Y Cf. A195284, A195360, A195361, A195362.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Sep 16 2011
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