geometry – How to deduce circle theorems in Wolfram language?


I can deduce the first one by applying FindGeometricConjectures on the following scene:

GeometricScene[{
    "A","B","C"
},{
    Line[{{"A","B"},{"B","C"}}],CircleThrough[{"A","B","C"},Midpoint[{"A","C"}]]
}]

Next one:

GeometricScene[{
    "A","B","C","D"
},{
    Line[{{"A","B"},{"B","C"},{"A","D"},{"D","C"}}],CircleThrough[{"A","B","C","D"}]
}]

But the following is not working:

GeometricScene[{
    "A","B","C","D"
},{
    Line[{{"A","B"},{"B","C"},{"A","D"},{"D","C"}}],CircleThrough[{"A","B","C"},"D"]
}]