Trim intersection circles at point of tangency in Illustrator CC

i am building a logo which is essentially a circle with a road passing through the middle of it. Normally, i would use autocad to do this, i find it much faster an easier to use, however, i am learning how to use adobe products (in this case Illustrator) with my new CC subscription.
I have used a number of intersection circles in order to generate the object, but am having problems trying to trim the unwanted interior circles at points of tangency. I want the dark outline to stay for the time being, as i intend to color the area inside the circle (excluding the road) orange.
The blue object in the background is the original favicon that i am copying. It is a bitmap that i want to vectorise.
I have worked out to get from the above to what is below...so am making progress. I simply didnt remember to box select all objects prior to attacking it with the "Shape Builder Tool". Now i need to figure out how to trim the unwanted arcs that are outside the colored area?

Congratulations, that's a very nice effect! Hope you'll check out more of the learning content offered in the Illustrator section. In particular, you may enjoy a tutorial on the Shape Builder tool that's structured as a game. How to use Shape Builder | Adobe Illustrator CC tutorials
To access other tutorials, go to the main Illustrator section. Learn Illustrator, get help and support | Adobe Illustrator CC. Then click on "Show all tutorials," followed by "Learn Essentials" right below the large image. You'll find plenty of tutorials here that show you how to learn features and create unique effects. Good luck!
Best,
Rita Amladi

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