Suppose that there is line $l$ that is tangent to an ellipse $A$ at point $\,P\,$.
The ellipse has the foci $F'$ and $F$.
One then creates two lines - each from each focus to the tangency point $\,P\,$ .
What I want to prove is that the acute degree formed at $P$ between $l$ and the line segment $F'P$ equals the acute degree formed between $l$ and the line segment $FP$ .
How would I be able to prove this?
(ellipse has a horizontal axis as a major axis.) (from Proving a property of an ellipse and a tangent line of the ellipse)
Is there any way to do this without using trigonometry? I do understand the answers there, but I also need purely geometric ones without calculus, vector and trigonometry...