%I #10 May 13 2017 14:27:28

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

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

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

%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)=(sqrt(7),3,4).

%C See A195284 for definitions and a general discussion.

%e (A)=1.75938215709649255886516352490038207092333...

%t a = Sqrt[7]; b = 3; c = 4;

%t 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) A195399 *)

%t N[x2, 100]

%t RealDigits[%] (* (B) A195400 *)

%t N[x3, 100]

%t RealDigits[%] (* (C) A195401 *)

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

%t RealDigits[%] (* Philo(ABC,I) A195402 *)

%Y Cf. A195284, A195400, A195401, A195402.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 17 2011