how to insert the projected edge on plane and how to take focus and intersection of edges on one plane during the sketch
see the attached image.
Unless I am misunderstanding what you are asking, what about
convert entities command in the sketch toolbar.
If you are after the outer edges, then use convert entities.
And if you after the interference of surface and plane, then use intersection curves.
If Scott and Deepak didn't answer your question, then I suspect that your front plane is not the sketch plane and the cylinder is not perpendicular to the sketch plane. If so, you need to make a sketch on the front plane and get the intersection curves on that plane, then use convert entities in the sketch shown in your picture to project those edge on to your sketch plane.
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