# [✓] Place a point out of a region using GeometricScene?

Posted 3 months ago
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 In a GeometricScene, I want a point to be out of a region. Say a triangle and a point B out of it. How can I do it?
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Posted 3 months ago
 Vasileios, I hope this might help.[Element] works well. However, [NotElement] doesn't work. I will expect for WL to support it. gs = GeometricScene[{"B", "X", "Y", "Z"}, {t = Triangle[{"X", "Y", "Z"}], "B" \[Element] t} ]; RandomInstance[gs]  gs = GeometricScene[{"B", "X", "Y", "Z"}, {t = Triangle[{"X", "Y", "Z"}], "B" \[NotElement] t} ]; RandomInstance[gs] But there is the following ugly way. gs = GeometricScene[{"B", "X", "Y", "Z"}, {p = Polygon[{"B", "X", "Y", "Z"}], GeometricAssertion[p, "Convex"], Triangle[{"X", "Y", "Z"}]} ]; RandomInstance[gs] 
Posted 2 months ago
 Thanks. I think The ugly way is the only way
Posted 2 months ago
 In fact, inspired by your Publish "computable famous theorems of geometry", I was trying to construct a right triangle and three squares with sides at triangle sides, trying the Pythagorean theorem. Any ideas?
 This should work for specifying that a point is not in a polygon, for instance: gs = GeometricScene[{"B", "X", "Y", "Z"}, { t == Triangle[{"X", "Y", "Z"}], SignedRegionDistance[t, "B"] > 0 }]; RandomInstance[gs] As for the Pythagorean theorem, see here.