2
$\begingroup$

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"]
}]
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3
  • $\begingroup$ With v12.1.1 on a Mac for the third example I get {EuclideanDistance["C", "D"] == EuclideanDistance["D", "A"]}. What result do you get that indicates that it is not working? $\endgroup$ – Bob Hanlon Sep 7 '20 at 0:39
  • 1
    $\begingroup$ @BobHanlon I also get the same on 12.1 but this is not the result I am after. This result is pretty obvious since CircleThrough[{"A","B","C"},"D"] means they are both radius. But the result I am after is PlanarAngle[{"A", "D", "C"}] == 2 PlanarAngle[{"A", "B", "C"}] $\endgroup$ – user13892 Sep 7 '20 at 3:50
  • $\begingroup$ Then I recommend that you edit your question to show what you tried, what you got, what you expected and why. $\endgroup$ – Bob Hanlon Sep 7 '20 at 3:53
3
$\begingroup$

It seems that MMA can not find the general result but a special situation such as PlanarAngle equal to 30 Degree.

Here is my test.

FindGeometricConjectures[
 RandomInstance@
  GeometricScene[{"A", "B", "C", 
    "D"}, {GeometricAssertion[{"C", "D"}, {"SameSide", 
      Line[{"A", "B"}]}], CircleThrough[{"A", "B", "C"}, "D"], 
    PlanarAngle[{"A", "C", "B"}, "Counterclockwise"] == 30 \[Degree], 
    Line[{{"D", "A"}, {"D", "B"}}]}]]

enter image description here

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