In[]:=
a={-4,2}
Out[]=
{-4,2}
In[]:=
b={0,-1}
Out[]=
{0,-1}
In[]:=
c={3,3}
Out[]=
{3,3}
In[]:=
GeometricScene[{a,b,c},{GeometricStep[{Line[{a,b}]}],​​GeometricStep[{CircleThrough[{b,c},a],CircleThrough[{a,c},b]}],​​GeometricStep[{Triangle[{a,b,c}]}]}]
Out[]=
GeometricScene[{{-4,2},{0,-1},{3,3}},{GeometricStep[{Line[{a,b}]}],GeometricStep[{CircleThrough[{b,c},a],CircleThrough[{a,c},b]}],GeometricStep[{Triangle[{a,b,c}]}]},{}]
In[]:=
TriangleMeasurement[{{-4,2},{0,-1},{3,3}},"Circumradius"]
Out[]=
5
2
In[]:=
TriangleConstruct[{{-4,2},{0,-1},{3,3}}]
Out[]=
Triangle[{{-4,2},{0,-1},{3,3}}]
In[]:=
Entity["WolframDemonstration","b1284e57"]["Manipulate"]
Out[]=
​
AP
0.55
PB
0.55
In[]:=
Entity["GeometricScene","ButterflyTheorem"]["RelatedDemonstrations"]
Out[]=

The Butterfly Theorem

In[]:=
GeometricScene[{a{-4,2},b{0,-1},​​c{3,3}},{GeometricStep[{Triangle[{a,b,c}],GeometricStep[{PerpendicularBisector[{b,c}],PerpendicularBisector[{a,b}]}]}]}]
Out[]=
GeometricScene[{{a,b,c},{}},{GeometricStep[{Triangle[{a,b,c}],GeometricStep[{PerpendicularBisector[{b,c}],PerpendicularBisector[{a,b}]}],a{-4,2},b{0,-1},c{3,3}}]},{}]
RandomInstance[​​GeometricScene[{a,b,c},{GeometricStep[{Line[{a,b}]}],​​GeometricStep[{CircleThrough[{b,c},a],CircleThrough[{a,c},b]}],​​GeometricStep[{Triangle[{a,b,c}]}]}]]