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A195384 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)=(2,sqrt(5),3).

%I A195384 #5 Mar 30 2012 18:57:45
%S A195384 1,7,4,8,0,6,4,0,9,7,7,9,5,2,8,4,2,8,3,1,9,7,2,0,4,8,2,0,2,2,3,0,2,0,
%T A195384 4,5,5,1,4,9,8,8,3,2,6,3,9,4,8,2,6,8,7,5,3,6,8,0,8,2,5,1,1,4,8,0,1,8,
%U A195384 6,1,9,6,0,1,7,7,1,3,1,1,8,2,4,9,3,8,6,0,5,7,4,0,5,1,6,5,8,7,2,2
%N A195384 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)=(2,sqrt(5),3).
%C A195384 See A195284 for definitions and a general discussion.
%e A195384 (C)=1.74806409779528428319720482022302045514988...
%t A195384 a = 2; b = Sqrt[5]; c = 3; f = 2 a*b/(a + b + c);
%t A195384 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195384 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195384 x3 = f*Sqrt[2]
%t A195384 N[x1, 100]
%t A195384 RealDigits[%]   (* (A) A195381 *)
%t A195384 N[x2, 100]
%t A195384 RealDigits[%]   (* (B) A195383 *)
%t A195384 N[x3, 100]
%t A195384 RealDigits[%]   (* (C) A195384 *)
%t A195384 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195384 RealDigits[%]   (* Philo(ABC,I) A195385 *)
%Y A195384 Cf. A195284.
%K A195384 nonn,cons
%O A195384 1,2
%A A195384 _Clark Kimberling_, Sep 17 2011