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Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(2,5,sqrt(29)).
5

%I #5 Mar 30 2012 18:57:45

%S 1,9,5,0,1,2,5,7,0,6,5,2,0,6,5,8,8,2,5,3,3,8,5,5,7,6,0,7,8,2,0,1,4,3,

%T 3,9,3,1,7,9,7,7,3,5,4,4,7,5,9,4,8,0,2,4,4,4,6,7,9,8,6,5,9,9,3,8,6,1,

%U 6,8,3,7,6,0,9,3,5,9,2,7,8,1,2,8,2,9,0,9,3,6,5,9,7,8,7,0,2,0,0,6

%N Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(2,5,sqrt(29)).

%C See A195284 for definitions and a general discussion.

%e (B)=1.950125706520658825338557607820143393179773544...

%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.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 16 2011