How to make a round button in android app?

Question

Android

I will deviate from the topic so that you understand the essence of the problem.
And so guys, I'll start with the fact that the practice is similar at the enterprise, we are developing mobile applications there. So today I fell into a stupor. I was given the task to find out and try to make non-standard buttons, I have never been engaged in design. I did everything, at the beginning of Imgbuttons, then I already found how to work with xml shapes, etc.
And now the task is to make a round button, and around it there are still buttons with rounded edges, in the princepe you can insert round images or xml, with android:shape="rectangle", into the background. But the button will still remain exactly square (well, that is, visually not, but the polygons from the standard button will remain), that is, you can’t move the second one directly close to it, but the task is such that you need it to be very close. that is, no or almost no spaces.
I know a similar question has already been How to make a round button in android? but maybe then consider the application that I found?
Here's an app I found to show what I'm talking about. What I need is done in this Smart IR Remote - AnyMote application .

That's what you think? How is it implemented in it and how can this be implemented?
Whether only by the: View method, in the onDraw method of which you draw a round button, and in the onKeyDown method you calculate the coordinates and decide whether the event should be processed or not, initiating an additional performClick to call subscriber handlers.

Answer 1

That is, even now I'm interested in how to put buttons close there, what layouts to use and how?