Maximize an angle by finding a point's coordinates

[theraginggod]

Point P is located somewhere between the EA-line. I have to find the coordinates of point P, so that the angle it creates with the given T1 and T2 points is maximal. Figure might not be 100% correctly drawed, but the coordinates are there. Thanks in advance!

 

[stapel]

Point P is located somewhere between the EA-line. I have to find the coordinates of point P, so that the angle it creates with the given T1 and T2 points is maximal. Figure might not be 100% correctly drawed, but the coordinates are there. Thanks in advance!View attachment 37003

What are your thoughts? What have you tried? How far have you gotten? ("Read Before Posting")

Please be complete. Thank you!

 

[Dr.Peterson]

Point P is located somewhere between the EA-line. I have to find the coordinates of point P, so that the angle it creates with the given T1 and T2 points is maximal. Figure might not be 100% correctly drawed, but the coordinates are there. Thanks in advance!View attachment 37003

It appears that you are using a notation in which points are designated by (x | y), so the actual layout would look like this, where the locations of A and E are swapped from the way you drew them:

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You haven't told us anything about what methods you can use, or what you've tried; do you want to use calculus, or just geometry or trigonometry? What have you learned that might be applicable? Also, where did the problem come from? If it's from a textbook or course, what topic is it associated with?

One geometrical idea I have involves the circle containing P, T₁, and T₂, if that suggests anything to you.