This is the 88th most frequent Turkish word.
çıkan
"Çıkan" means "emerging," "coming out," or "produced."
In this sentence, 'çıkan' is the present participle form of the verb 'çıkmak', which means 'to exit' or 'to come out'. It is used as a modifier describing the noun 'kişi' (person) as 'the one who comes out (exits)'.
Kapıdan çıkan kişi öğretmendi.
The person who exited the door was the teacher.
Here, 'çıkan' is again the present participle of 'çıkmak', used to describe 'çözüm' (solution) as 'the one that emerges or arises'.
Soruları çözmek için bir çözüm çıkan grup öğrencilere yardım etti.
The group that provided a solution to solve the questions helped the students.
In this usage, 'çıkan' modifies the noun 'güneş' (the sun) as 'the one that comes out or emerges'.