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A195397 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).

%I A195397 #5 Mar 30 2012 18:57:45
%S A195397 1,6,1,1,7,6,7,4,0,2,9,5,1,5,5,7,4,3,0,1,9,6,1,7,7,6,1,9,1,3,8,6,0,9,
%T A195397 9,2,5,6,8,5,5,0,2,6,1,9,9,8,1,8,8,6,9,5,5,2,9,0,1,9,7,4,2,0,0,4,3,5,
%U A195397 5,4,8,1,6,0,9,6,5,5,3,2,4,7,8,8,4,1,0,7,5,4,1,4,8,3,9,4,0,5,3,0
%N A195397 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).
%C A195397 See A195284 for definitions and a general discussion.
%e A195397 (C)=1.6117674029515574301961776191386099256...
%t A195397 a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
%t A195397 f = 2 a*b/(a + b + c);
%t A195397 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195397 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195397 x3 = f*Sqrt[2]
%t A195397 N[x1, 100]
%t A195397 RealDigits[%]    (* (A) A195395 *)
%t A195397 N[x2, 100]
%t A195397 RealDigits[%]    (* (B) A195396 *)
%t A195397 N[x3, 100]
%t A195397 RealDigits[%]    (* (C) A195397 *)
%t A195397 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195397 RealDigits[%]    (*  Philo(ABC,I) A195398 *)
%Y A195397 Cf. A195284.
%K A195397 nonn,cons
%O A195397 1,2
%A A195397 _Clark Kimberling_, Sep 17 2011