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A195400 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(7),3,4).

%I A195400 #9 May 13 2017 14:47:43
%S A195400 1,8,0,5,6,6,4,9,1,8,5,8,0,5,4,5,8,7,9,3,3,1,1,7,8,9,9,5,1,4,7,6,5,2,
%T A195400 7,6,5,7,1,9,6,5,4,4,2,2,5,5,6,7,3,3,0,9,2,8,4,2,2,2,0,7,2,1,0,6,5,2,
%U A195400 4,1,5,6,9,0,2,6,2,8,8,4,9,6,3,1,9,4,7,6,1,5,1,3,6,7,2,7,5,1,8,5
%N A195400 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(7),3,4).
%C A195400 See A195284 for definitions and a general discussion.
%e A195400 (B)=1.80566491858054587933117899514765276...
%t A195400 a = Sqrt[7]; b = 3; c = 4;
%t A195400 f = 2 a*b/(a + b + c);
%t A195400 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195400 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195400 x3 = f*Sqrt[2]
%t A195400 N[x1, 100]
%t A195400 RealDigits[%]    (* (A) A195399 *)
%t A195400 N[x2, 100]
%t A195400 RealDigits[%]    (* (B) A195400 *)
%t A195400 N[x3, 100]
%t A195400 RealDigits[%]    (* (C) A195401 *)
%t A195400 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195400 RealDigits[%]    (*  Philo(ABC,I) A195402 *)
%Y A195400 Cf. A195284.
%K A195400 nonn,cons
%O A195400 1,2
%A A195400 _Clark Kimberling_, Sep 17 2011