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A195387 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)).

%I A195387 #10 Dec 24 2017 09:25:45
%S A195387 1,1,4,6,8,0,9,7,5,9,1,5,8,1,9,1,6,3,0,9,5,3,7,7,6,0,0,6,5,1,9,6,8,1,
%T A195387 6,0,7,5,5,6,7,6,8,2,9,7,3,5,9,7,5,1,3,7,2,7,2,9,8,2,4,8,5,3,3,1,7,8,
%U A195387 9,4,6,4,4,3,9,9,1,8,6,0,9,3,6,7,6,2,0,5,1,5,2,1,5,4,4,9,5,5,0,7
%N A195387 Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)).
%C A195387 See A195284 for definitions and a general discussion.
%H A195387 G. C. Greubel, <a href="/A195387/b195387.txt">Table of n, a(n) for n = 1..10000</a>
%e A195387 (B)=1.1468097591581916309537760065196816075567682...
%t A195387 a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];
%t A195387 f = 2 a*b/(a + b + c);
%t A195387 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195387 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195387 x3 = f*Sqrt[2]
%t A195387 N[x1, 100]
%t A195387 RealDigits[%]   (* (A) A195386 *)
%t A195387 N[x2, 100]
%t A195387 RealDigits[%]   (* (A) A195387 *)
%t A195387 N[x3, 100]
%t A195387 RealDigits[%]   (* (A) A195388 *)
%t A195387 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195387 RealDigits[%]   (* Philo(ABC,I) A195389 *)
%Y A195387 Cf. A195284, A195386, A195388, A195389.
%K A195387 nonn,cons
%O A195387 1,3
%A A195387 _Clark Kimberling_, Sep 17 2011