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A195367 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(2),sqrt(3),sqrt(5)).

%I A195367 #9 Dec 24 2017 09:24:15
%S A195367 1,2,8,7,2,1,2,0,8,2,6,1,4,7,9,8,7,6,6,1,9,8,3,9,0,5,3,0,2,7,3,1,7,2,
%T A195367 8,5,8,2,4,6,3,9,2,3,4,1,3,3,1,4,5,3,3,0,1,5,7,5,1,8,7,7,1,4,4,5,8,3,
%U A195367 6,5,9,3,8,8,1,8,0,7,6,8,0,5,1,9,5,6,1,1,3,2,4,7,2,5,3,3,9,9,3,9
%N A195367 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(2),sqrt(3),sqrt(5)).
%C A195367 See A195284 for definitions and a general discussion.
%H A195367 G. C. Greubel, <a href="/A195367/b195367.txt">Table of n, a(n) for n = 1..10000</a>
%e A195367 (C)=1.2872120826147987661983905302731728582463923413314...
%t A195367 a = Sqrt[2]; b = Sqrt[3]; c = Sqrt[5];
%t A195367 f = 2 a*b/(a + b + c);
%t A195367 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195367 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195367 x3 = f*Sqrt[2]
%t A195367 N[x1, 100]
%t A195367 RealDigits[%]    (* (A) A195365 *)
%t A195367 N[x2, 100]
%t A195367 RealDigits[%]    (* (B) A195366 *)
%t A195367 N[x3, 100]
%t A195367 RealDigits[%]    (* (C) A195367 *)
%t A195367 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195367 RealDigits[%]    (* Philo(ABC,I) A195368 *)
%Y A195367 Cf. A195284.
%K A195367 nonn,cons
%O A195367 1,2
%A A195367 _Clark Kimberling_, Sep 16 2011