Equal incircles theorem

Okay kiddo, so you know how a circle is a round shape with no corners? Well, imagine you draw a triangle with three sides and three corners. The equal incircles theorem says that you can draw a circle inside the triangle that touches all three sides of the triangle. And the cool thing is, no matter what size or shape the triangle is, you can always draw a circle that fits perfectly inside it like this.

Now, imagine you draw another triangle that looks very different from the first one. You can still draw a circle inside that one too, and it will touch all three sides in the same way as the first one. And, guess what? If both triangles have the same size circle inside them, they must be exactly the same shape and size!

So, this is the equal incircles theorem - it tells us that any triangle can have a circle that touches all three sides, and if two triangles have the same size circle inside, they must be the same shape and size themselves. Pretty neat, huh?