geometry problem

[Guest]

Hello
Can someone halp me solving this problem? All tips are welcome! You don't have to type out a solution, just tell me how to get somewhere. Thanks!

Consider a triangle ABC with [tex]\angle[/tex]C=90° , and call its centroid G. Let P be a point on the half-line [AG such that [tex]\angle[/tex]CPA = [tex]\angle[/tex]CAB and Q be a point on the half-line [BG such that [tex]\angle[/tex]CQB= [tex]\angle[/tex]ABC . Show that the circumcircles of [tex]\triangle[/tex]AQG and [tex]\triangle[/tex]BPG intersect at AB.

[Guest]

Maybe I'm missing something but... are you sure this construction is even possible?

https://www.geogebra.org/geometry/pvhx68j9