If we use GeometricSolveValues in version 14.0, we can use this code to get a ConditionalExpression expr:
RandomInstance[ sence = GeometricScene[{{P -> {0, 0}, X, Y, Z}, {p -> 3, q -> 2}}, {circle = Circle[P, {p, q}], X ∈ circle, Y ∈ circle, Z ∈ circle, GeometricAssertion[Triangle[{X, Y, Z}], "Equilateral"]}], RandomSeeding -> 1]expr = GeometricSolveValues[sence, EuclideanDistance[X, Y]]Image may be NSFW.
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How can I compute the maximum value of the expr in MMA?
