Now I'm going to draw octagons, both inscribed and circumscribed. I'll begin by drawing a circle on the line and then draw another circle from the left quadrant over to the right. And then do that again symmetrically from the right to the left. This creates a vesicle discuss, draw a line through the vertical center to create the cross axis. I'm going to color the original circle, black for clarity. Now create additional circles from the top of this central circle to the bottom and again from the bottom to the top.
Now we have cross quarter points at 45 degree increments. Draw an X through the center like this. Now I'm going to switch to red. And I'll use a thick line Wait, draw in the octagon, which is inscribed in this black circle. Next, I'd like to draw an octagon that circumscribed about that circle. So to do that, we need to draw some additional construction circles.
I'm going to start at the top quadrant of the original circle, and draw a circle down to the center. And then do the same thing on the bottom and on the left, and on the right, draw another circle from the center out and snap it to this intersection point. Then we can draw in a square actually I'm going to draw that in another color. I'll use black But with a thin or regular line Wait. I'll make it thin. And then draw in a line from that point over to the corresponding point on the right.
And then draw another one down and over and back up to create a square that circumscribes the circle. Then draw another square starting up here and going down to this point and then work your way around. To create a square at a 45 degree angle. I'm going to zoom in there now and choose a thick line wait. This time I'll choose a darker red color. Now I can draw in the circumscribed octagon by carefully tracing over these points, and you have to be a little bit careful because there are so many different intersection points here.
And this is where the Apple Pencil comes in handy. If you're using your finger, you might have to zoom in a little closer on each one of those points in order to connect it correctly. Finally, I'm going to draw in a symbol called the Okta Graham star in the in inscribed octagon. And one way to do this is to start drawing from a vertex and then skip to there's one, two, I'm going to skip those and go over here. Now skip two and go down here. That creates this pattern.