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I have a circle feature class and want to split it in 4 segments, where it intersects with a point feature class (see image).

What would be the best tool to do it?

If it is an Arc (line) then PointOnLineOverlayer will do it. If it is an Ellipse or Circle (area) then use a GeometryCoercer to coerce the area geometry into a line (fme_line) and the PointOnLineOverlayer.

I've attached an example built in FME 2017: splitcirclesexample.fmw

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