Plane and Circle Intersection
Intersecting a plane and a circle will actually create two points as seen below. It should be noted that the plane and circle cannot be parallel or coplanar.
To Create Points at the Intersection of a Plane and Circle:
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From the menu, select Construct> New Points>Intersection>Plane and Circle Intersection.
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Select the plane, then the circle. Two new points will be created in the active collection’s Intersections group named Plane-Circle1 and Plane-Circle2.