는 (관형사형 전성 어미)

We've seen the Future/Uncertain Tense; we've seen the Past/Completed Tense. What is left is the present tense.

You only ever see this with true 동사, never 형용사. The reason why, in my mind, is that the 형용사 are atomic events. That is, you never, ever use them to describe a process of becoming. That's what 되다 is for: that rare case when you want to talk about how something transitions into something else.

The 는 ending conveys a sense of progressive action. "읽는 첵" is not just a book that is read, it is a book that is being read right now, that is, someone is holding the book and turning the pages as we speak. We might translate it as "book that (someone) reads", but really, it should probably be more accurately translated as "book that (someone) is reading".

Of course, as always, a precise translation is clumsy and all but impossible in English.