(({{-1, 1, \[Placeholder], 1, 1, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder]}, {1, -1, 1, 1, \[Placeholder], 1, \[Placeholder], 0, 0, 0, \[Placeholder], \[Placeholder], 0, \[Placeholder]}, {\[Placeholder], 1, -1, 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], 0, \[Placeholder]}, {1, 1, 1, -1, 1, \[Placeholder], 1, \[Placeholder], 0, 0, 0, 0, \[Placeholder], 0}, {1, \[Placeholder], \[Placeholder], 1, -1, 1, \[Placeholder], 0, \[Placeholder], \[Placeholder], \[Placeholder], 0, \[Placeholder], 0}, {\[Placeholder], 1, \[Placeholder], \[Placeholder], 1, -1, 1, 0, \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 0, 0}, {\[Placeholder], \[Placeholder], 1, 1, \[Placeholder], 1, -1, \[Placeholder], \[Placeholder], \[Placeholder], 0, \[Placeholder], 0, 0}, {0, 0, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], -1, 1, \[Placeholder], \[Placeholder], 1, 1, 1}, {0, 0, \[Placeholder], 0, \[Placeholder], \[Placeholder], \[Placeholder], 1, -1, 1, \[Placeholder], 1, \[Placeholder], \[Placeholder]}, {\[Placeholder], 0, 0, 0, \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 1, -1, 1, \[Placeholder], 1, \[Placeholder]}, {\[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, \[Placeholder], \[Placeholder], 1, -1, \[Placeholder], 1, 1}, {0, \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 1, 1, \[Placeholder], \[Placeholder], -1, \[Placeholder], 1}, {\[Placeholder], 0, 0, \[Placeholder], \[Placeholder], 0, 0, 1, \[Placeholder], 1, 1, \[Placeholder], -1, 1}, {\[Placeholder], \[Placeholder], \[Placeholder], 0, 0, 0, 0, 1, \[Placeholder], \[Placeholder], 1, 1, 1, -1}}))

bilval[a_,b_]:=1/2((evars[[a,3]]^2+evars[[a,2]]^2-1)*(evars[[b,1]]+evars[[b,2]])/(evars[[a,1]]+evars[[a,2]])+(evars[[b,3]]^2+evars[[b,2]]^2-1)*(evars[[a,1]]+evars[[a,2]])/(evars[[b,1]]+evars[[b,2]]))-evars[[a,3]]*evars[[b,3]]-evars[[a,2]]*evars[[b,2]]

bil[a_,b_]:=1/2((vars[[a,3]]^2+vars[[a,2]]^2-1)*(vars[[b,1]]+vars[[b,2]])/(vars[[a,1]]+vars[[a,2]])+(vars[[b,3]]^2+vars[[b,2]]^2-1)*(vars[[a,1]]+vars[[a,2]])/(vars[[b,1]]+vars[[b,2]]))-vars[[a,3]]*vars[[b,3]]-vars[[a,2]]*vars[[b,2]]==matzeros[[a,b]]

matzeros=(({{\[Placeholder], 1, \[Placeholder], \[Placeholder], \[Placeholder], 0, 0, \[Placeholder], \[Placeholder], \[Placeholder]}, {1, \[Placeholder], 1, 1, \[Placeholder], 0, 0, 0, \[Placeholder], 0}, {\[Placeholder], 1, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 0, 0, 0}, {\[Placeholder], 1, \[Placeholder], \[Placeholder], 1, 0, \[Placeholder], \[Placeholder], \[Placeholder], 0}, {\[Placeholder], \[Placeholder], 1, 1, \[Placeholder], \[Placeholder], \[Placeholder], \[Placeholder], 0, 0}, {0, 0, \[Placeholder], 0, \[Placeholder], \[Placeholder], 1, \[Placeholder], \[Placeholder], 1}, {0, 0, \[Placeholder], \[Placeholder], \[Placeholder], 1, \[Placeholder], 1, \[Placeholder], \[Placeholder]}, {\[Placeholder], 0, 0, \[Placeholder], \[Placeholder], \[Placeholder], 1, \[Placeholder], 1, 1}, {\[Placeholder], \[Placeholder], 0, \[Placeholder], 0, \[Placeholder], \[Placeholder], 1, \[Placeholder], 1}, {\[Placeholder], 0, 0, 0, 0, 1, \[Placeholder], 1, 1, \[Placeholder]}}))
vars=(({{1, 1, a141}, {1, a52, a142}, {1, a53, a143}, {a46, 1, 0}, {1, a57, 0}, {a48, 0, 1}, {0, a59, a149}, {0, a510, a1410}, {0, a511, 1}, {a413, a513, 1}}))
Solve[bil[1,2]&&bil[1,6]&&bil[1,7]&&bil[2,3]&&bil[2,4]&&bil[2,6]&&bil[2,7]&&bil[2,8]&&bil[2,10]&&bil[3,5]&&bil[3,8]&&bil[3,9]&&bil[3,10]&&bil[4,5]&&bil[4,6]&&bil[4,10]&&bil[5,9]&&bil[5,10]&&bil[6,7]&&bil[6,10]&&bil[7,8]&&bil[8,9]&&bil[8,10]&&bil[9,10]]

bil[1,2]&&bil[1,6]&&bil[1,7]&&bil[2,3]&&bil[2,4]&&bil[2,6]&&bil[2,7]&&bil[2,8]&&bil[2,10]&&bil[3,5]&&bil[3,8]&&bil[3,9]&&bil[3,10]&&bil[4,5]&&bil[4,6]&&bil[4,10]&&bil[5,9]&&bil[5,10]&&bil[6,7]&&bil[6,10]&&bil[7,8]&&bil[8,9]&&bil[8,10]&&bil[9,10]

{a141,a1410,a142,a143,a149,a413,a46,a48,a510,a511,a513,a52,a53,a57,a59}/. %32

RootApproximant[{2.613125929752752`,2.4142135623730954`,1.8477590650225744`,2.613125929752752`,2.4142135623730954`,1.530733729460355`,1.8284271247461907`,1.530733729460355`,6.308644059797901`,8.921769989550652`,3.6955181300451487`,2.4142135623730954`,10.656854249492381`,5.828427124746191`,2.613125929752752`}]

Solve[bil[1,2]&&bil[1,6]&&bil[1,7]&&bil[2,3]&&bil[2,4]&&bil[2,6]&&bil[2,7]&&bil[2,8]&&bil[2,10]&&bil[3,5]&&bil[3,8]&&bil[3,9]&&bil[3,10]&&bil[4,5]&&bil[4,6]&&bil[4,10]&&bil[5,9]&&bil[5,10]&&bil[6,7]&&bil[6,10]&&bil[7,8]&&bil[8,9]&&bil[8,10]&&bil[9,10]]

Clear[a141,a1410,a142,a143,a149,a413,a46,a48,a510,a511,a513,a52,a53,a57,a59]

N[%35]

{a141,a1410,a142,a143,a149,a413,a46,a48,a510,a511,a513,a52,a53,a57,a59}={4 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2)),1+(Sqrt[2]),3 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2)),4 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2)),1+(Sqrt[2]),2 (Sqrt[2-(Sqrt[2])]),-1+2 (Sqrt[2]),2 (Sqrt[2-(Sqrt[2])]),10 (Sqrt[2-(Sqrt[2])])-3 (((2-(Sqrt[2])))^(3/2)),2 (7 (Sqrt[2-(Sqrt[2])])-2 (((2-(Sqrt[2])))^(3/2))),2 (3 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2))),1+(Sqrt[2]),5+4 (Sqrt[2]),3+2 (Sqrt[2]),4 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2))}

Simplify[{4 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2)),1+(Sqrt[2]),3 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2)),4 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2)),1+(Sqrt[2]),2 (Sqrt[2-(Sqrt[2])]),-1+2 (Sqrt[2]),2 (Sqrt[2-(Sqrt[2])]),10 (Sqrt[2-(Sqrt[2])])-3 (((2-(Sqrt[2])))^(3/2)),2 (7 (Sqrt[2-(Sqrt[2])])-2 (((2-(Sqrt[2])))^(3/2))),2 (3 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2))),1+(Sqrt[2]),5+4 (Sqrt[2]),3+2 (Sqrt[2]),4 (Sqrt[2-(Sqrt[2])])-(((2-(Sqrt[2])))^(3/2))}]

{a141,a1410,a142,a143,a149,a413,a46,a48,a510,a511,a513,a52,a53,a57,a59}={(Sqrt[2-(Sqrt[2])]) (2+(Sqrt[2])),1+(Sqrt[2]),(Sqrt[2-(Sqrt[2])]) (1+(Sqrt[2])),(Sqrt[2-(Sqrt[2])]) (2+(Sqrt[2])),1+(Sqrt[2]),2 (Sqrt[2-(Sqrt[2])]),-1+2 (Sqrt[2]),2 (Sqrt[2-(Sqrt[2])]),(Sqrt[2-(Sqrt[2])]) (4+3 (Sqrt[2])),2 (Sqrt[2-(Sqrt[2])]) (3+2 (Sqrt[2])),2 (Sqrt[2-(Sqrt[2])]) (1+(Sqrt[2])),1+(Sqrt[2]),5+4 (Sqrt[2]),3+2 (Sqrt[2]),(Sqrt[2-(Sqrt[2])]) (2+(Sqrt[2]))}

bilval[a_,b_]:=1/2((evars[[a,3]]^2+evars[[a,2]]^2-1)*(evars[[b,1]]+evars[[b,2]])/(evars[[a,1]]+evars[[a,2]])+(evars[[b,3]]^2+evars[[b,2]]^2-1)*(evars[[a,1]]+evars[[a,2]])/(evars[[b,1]]+evars[[b,2]]))-evars[[a,3]]*evars[[b,3]]-evars[[a,2]]*evars[[b,2]]

evars=(({{1, 1, a141}, {1, a52, a142}, {1, a53, a143}, {-1, 1, 0}, {1, -1, 0}, {a46, 1, 0}, {1, a57, 0}, {a48, 0, 1}, {0, a59, a149}, {0, a510, a1410}, {0, a511, 1}, {0, 0, 1}, {a413, a513, 1}, {0, 0, -1}}))

Graphics[{Table[Circle[{vars[[i,3]]/(vars[[i,1]]+vars[[i,2]]),vars[[i,2]]/(vars[[i,1]]+vars[[i,2]])},1/(vars[[i,1]]+vars[[i,2]])],{i,Length[vars]}],Line[{{0,-0.7},{0,1.4}}],Line[{{1.7,0},{-0.3,0}}],Line[{{1.7,1},{-0.3,1}}],Line[{{a141/2,-0.7},{a141/2,1.4}}]}]

bilval[6,13]
N[2/149(26+Sqrt[853374])]

Simplify[bilval[1,11]]