%I #6 Mar 30 2012 18:57:45

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

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

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

%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)=(2,3,sqrt(13)).

%C See A195284 for definitions and a general discussion.

%e (A)=1.45696410161448598385109158713926698408228516810...

%t a = 2; b = 3; c = Sqrt[13]; 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) A195355 *)

%t N[x2, 100]

%t RealDigits[%](* (B) A195356 *)

%t N[x3, 100]

%t RealDigits[%](* (C) A195357 *)

%t N[(x1 + x2 + x3)/(a + b + c), 100]

%t RealDigits[%](* Philo(ABC,I) A195358 *)

%Y Cf. A195284, A195345, A195346, A195347.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 16 2011