Hello friends, I’m new here, and for my first post, I will share my experiences regarding Facebook reach and engagement, which is a common struggle for many people.
http://i1.imgcry.com/2014/12/14/ornek.png
In post number 1, what I did was tag a page. I added the official page of the person who said the quote in the post (Alper Ayyıldız) as a tag, and it reflected positively on engagement, especially since the likes increased.
In post number 2, there was again a song lyric, but this time I added the person singing the lyric with a hashtag (#Allame). The result was slightly higher reach, and engagement as usual.
In post number 3, almost the entire graph in the “reach” section is dark because the people reaching this post were “non-likers/non-fans”. I shared this post in a group related to the page’s content, and since the people in the group saw/reached the post, the reach increased, but engagement was as usual.
These are just experiences because my page has only 2,800 likes 
It is hard to speak definitively since the number of likes is low, but since I make such posts at certain intervals, it works for me, even if on a small scale. Maybe you can benefit from this too. Maybe there are owners of 100k+ pages among you who use these methods, find them useful, rush to their computers, open this topic, and say “Sir, thank you very much, your tactic worked. Give me your page link so I can promote you :)” and I would give my page link without any hesitation. 
Additionally;
Addendum-1: If the page you tag is “verified,” the reach seriously skyrockets. There is no need to post a screenshot, but it hasn’t failed in 3 posts. While there is a reach of 200-300 when I tag a normal page, when the page I tag is verified, the reach hovers between “800-900”.
Addendum-2; Especially in posts suitable for sharing or where users are likely to share, add your own page’s name as a “tag” and see the result. Even if this isn’t effective on its own, it increases reach and engagement in a good way.
Addendum-3; As I have learned, increasing your page’s “Talking About This” count ensures that your posts fall onto the news feed of those who like your page more frequently. If we base this on the explanation made by Facebook regarding “Talking About This,” we know how to increase this number.
