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A195388 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(5),sqrt(7)).

%I A195388 #11 Dec 24 2017 09:27:42
%S A195388 1,4,2,0,6,2,0,2,7,3,3,9,4,4,3,7,9,4,6,4,1,5,1,4,4,8,1,2,1,1,6,1,6,9,
%T A195388 2,3,1,9,6,3,5,3,5,3,3,1,5,4,6,4,8,9,8,8,0,5,5,3,7,5,9,3,8,5,4,7,2,5,
%U A195388 5,9,2,8,2,3,3,2,2,9,9,1,9,3,3,6,7,4,3,8,2,1,3,1,8,4,9,2,0,7,2,3
%N A195388 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(5),sqrt(7)).
%C A195388 See A195284 for definitions and a general discussion.
%H A195388 G. C. Greubel, <a href="/A195388/b195388.txt">Table of n, a(n) for n = 1..10000</a>
%e A195388 (C)=1.420620273394437946415144812116169231963535...
%t A195388 a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];
%t A195388 f = 2 a*b/(a + b + c);
%t A195388 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195388 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195388 x3 = f*Sqrt[2]
%t A195388 N[x1, 100]
%t A195388 RealDigits[%]   (* (A) A195386 *)
%t A195388 N[x2, 100]
%t A195388 RealDigits[%]   (* (A) A195387 *)
%t A195388 N[x3, 100]
%t A195388 RealDigits[%]   (* (A) A195388 *)
%t A195388 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195388 RealDigits[%]   (* Philo(ABC,I) A195389 *)
%Y A195388 Cf. A195284, A195386, A195387, A195389.
%K A195388 nonn,cons
%O A195388 1,2
%A A195388 _Clark Kimberling_, Sep 17 2011