I'd like to show you another method for constructing a regular pentagram or Pentagon. And this one comes from 19th century Japan. I have a horizontal line. And I'll start by drawing a circle on it. And then I'll go ahead and label the points. Draw a circle from C to B.

Add a new label and then add another circle from D to C. So now we have three equally sized circles. I'll draw a circle encompassing all of them centered at C. What the radius AC I need to put in a perpendicular to the horizontal line running through C. I'll label its points of intersection. Next, draw a line from F to be analyzed from F to D. This creates new points as shown, draw a new circle from F to i and j and another one from F to G and H. This creates all the points we need for the Pentagon or pentagram. I'll label these. Now we just need to draw in the Pentagon actually I'll choose bright red for that with a thick line and I'll put a pentagram inside of that. Just to prove that this is a regular form where all the edges are equal, I'll just go ahead and measure those ek should equal k m and then k m should equal MN, MN, N, NL are equal and L and L e are equal.

And finally, l e is equal to ek so I've proven that we have a regular pentagram and Pentagon