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A195360 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)=(2,5,sqrt(29)).

%I A195360 #5 Mar 30 2012 18:57:45
%S A195360 1,9,5,0,1,2,5,7,0,6,5,2,0,6,5,8,8,2,5,3,3,8,5,5,7,6,0,7,8,2,0,1,4,3,
%T A195360 3,9,3,1,7,9,7,7,3,5,4,4,7,5,9,4,8,0,2,4,4,4,6,7,9,8,6,5,9,9,3,8,6,1,
%U A195360 6,8,3,7,6,0,9,3,5,9,2,7,8,1,2,8,2,9,0,9,3,6,5,9,7,8,7,0,2,0,0,6
%N A195360 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)=(2,5,sqrt(29)).
%C A195360 See A195284 for definitions and a general discussion.
%e A195360 (B)=1.950125706520658825338557607820143393179773544...
%t A195360 a = 2; b = 5; c = Sqrt[29]; f = 2 a*b/(a + b + c);
%t A195360 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t A195360 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t A195360 x3 = f*Sqrt[2]
%t A195360 N[x1, 100]
%t A195360 RealDigits[%]    (* (A) A195359 *)
%t A195360 N[x2, 100]
%t A195360 RealDigits[%]    (* (B) A195360 *)
%t A195360 N[x3, 100]
%t A195360 RealDigits[%]    (* (C) A195361 *)
%t A195360 N[(x1 + x2 + x3)/(a + b + c), 100]
%t A195360 RealDigits[%]    (* Philo(ABC,I)  A195362 *)
%Y A195360 Cf. A195284.
%K A195360 nonn,cons
%O A195360 1,2
%A A195360 _Clark Kimberling_, Sep 16 2011