Intersect Polygon and Segment
Tool (.ggt): http://www.geogebratube.org/material/show/id/97764
I continue to use the same definition of inside as IsInRegion[]. (more: http://www.geogebratube.org/student/m96425). Drag point M to see if GGB agrees with how it has shaded Jerome. I think you will find the orange segments and M always agree.