RegionIntersection of lines and circles

Questions
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1

Hi, I have some Circles and some Lines and I am trying to find their RegionIntersection. See attached notebooks for detail.
The Circle is this:

oic = Circle[{0, 0}, 7.5];

The three Lines are these:

ln1 = Line[{{0, 0}, {8, 0}}];
ln2 = Rotate[ln1, Pi/9, {0, 0}];
ln3 = Line[{{0, N[7.5*Sin[Pi/9]]}, {7.5, N[7.5*Sin[Pi/9]]}}]
Line[{0, 2.56515}, {7.5, 2.56515}]

Mathematica has a hard time to find the RegionIntersection of the Circle and the rotated Line. I understand that RegionIntersection can work with just identical Heads. What I do not understand why Graphics is able to deal with the rotated Line and display it correctly but RegionIntersection is not. Any good suggestion for a workaround?

RegionIntersection.nb (10 KB)

2

Yes, it is very irritating. These versions work:

ln1 = Line[{{0, 0}, {8, 0}}];
RegionIntersection[ln1, Rotate[DiscretizeRegion@ln1, Pi/9, {0, 0}]]
RegionIntersection[ln1, Rotate[Region@ln1, Pi/9, {0, 0}]]
3

Thanks a lot, it saves me from some headaches.