I recently needed to draw 3 groups of 5 blue circles and 4 yellow circles. What a chore! Can geogebra help? Here is how.
1) Close the algebra pane and in options -> labelling click no new objects.
2) Right click the screen and uncheck axes.
3) Go into options -> advanced, find preferences default and then point and uncheck show object.
4) Use the Center with center and radius tool and make a circle with a radius of 2.
5) Right click the circle and go into the color tab. Now choose a nice blue and set opacity to about 80.
6) You should have a nice blue circle on your screen.
7) Now go into tools and select Circle c: With Center B and radius 2. It may be slightly different in yours but it will be the only object there.
8) Click next and select Point B. Give the tool name blue and make sure show in toolbar is checked. Click finish. You get a message saying it was done and in the toolbar will be the tool.
9) Make a tool called yellow that makes a circle of radius 2 and is colored red in the same way.
10) Click the blue tool in the toolbar and everywhere you click the screen you will create a blue circle. Make 15 of them. You will have to scale the screen smaller to see them all.
11) Delete any blue circles on the screen and click the yellow tool. Make 12 of them. See the drawing below.
Easy with geogebra!
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.