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A195383 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)=(2,sqrt(5),3).

%I A195383 #6 Mar 30 2012 18:57:45
%S A195383 1,3,5,4,0,4,4,6,2,7,7,7,2,8,4,5,8,7,1,2,8,3,3,4,4,5,0,9,1,0,4,2,8,7,
%T A195383 1,2,4,0,6,0,4,5,8,0,9,0,6,6,0,7,0,3,6,1,9,9,7,8,9,0,3,6,6,7,7,8,5,9,
%U A195383 7,3,8,2,3,2,1,1,8,6,9,5,5,8,9,3,8,1,4,2,5,6,0,7,7,6,8,9,8,9,8,3
%N A195383 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)=(2,sqrt(5),3).
%C A195383 See A195284 for definitions and a general discussion.
%e A195383 (B)=1.354044627772845871283344509104287124060458090...
%t A195383 a = 2; b = Sqrt[5]; c = 3; f = 2 a*b/(a + b + c);
%t A195383 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195383 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195383 x3 = f*Sqrt[2]
%t A195383 N[x1, 100]
%t A195383 RealDigits[%]   (* (A) A195381 *)
%t A195383 N[x2, 100]
%t A195383 RealDigits[%]   (* (B) A195383 *)
%t A195383 N[x3, 100]
%t A195383 RealDigits[%]   (* (C) A195384 *)
%t A195383 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195383 RealDigits[%]   (* Philo(ABC,I) A195385 *)
%Y A195383 Cf. A195284.
%K A195383 nonn,cons
%O A195383 1,2
%A A195383 _Clark Kimberling_, Sep 17 2011