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A195401 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(7),3,4).

%I A195401 #8 May 13 2017 14:27:13
%S A195401 2,3,2,7,4,4,3,8,2,4,4,0,0,8,4,6,3,3,6,7,8,2,0,6,0,0,0,8,1,0,6,8,5,1,
%T A195401 2,2,3,1,8,6,3,4,7,9,3,2,4,0,1,7,7,8,8,7,3,1,2,7,0,6,5,7,2,9,3,2,9,3,
%U A195401 0,2,6,7,7,8,4,4,8,3,1,9,8,9,1,2,6,4,2,2,3,6,0,8,6,6,7,3,7,9,9,8
%N A195401 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(7),3,4).
%C A195401 See A195284 for definitions and a general discussion.
%e A195401 (C)=2.32744382440084633678206000810685122318...
%t A195401 a = Sqrt[7]; b = 3; c = 4;
%t A195401 f = 2 a*b/(a + b + c);
%t A195401 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195401 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195401 x3 = f*Sqrt[2]
%t A195401 N[x1, 100]
%t A195401 RealDigits[%]    (* (A) A195399 *)
%t A195401 N[x2, 100]
%t A195401 RealDigits[%]    (* (B) A195400 *)
%t A195401 N[x3, 100]
%t A195401 RealDigits[%]    (* (C) A195401 *)
%t A195401 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195401 RealDigits[%]    (*  Philo(ABC,I) A195402 *)
%Y A195401 Cf. A195284.
%K A195401 nonn,cons
%O A195401 1,1
%A A195401 _Clark Kimberling_, Sep 17 2011