When working with carbide bits, they are super for drilling holes, but as they are carbide, they will break. When drilling things out like you did Greg, I found it works best to use a Dremel with the separate speed control to slow it way down. Then let the Dremel and drill do the work. When you try to drill the holes by hand it is almost impossible to keep from moving the bit side to side and such. Also if you put any force on the bit it will snap immediately. Here is an example:
Clear plastic is usually harder and more brittle than colored plastics. I used one drill bit to drill all the holes without any trouble, but used my Dremel and just drilled the holes straight through at the panel line.
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To slow the Dremel down I use the very old separate speed control which makes drilling holes in plastic a breeze. It also helps when cutting grinding and doing just about anything as Dremels always run too fast, even the ones with speed control on them (like the one below) Note that the speed control on the Dremel itself is at full speed. The separate speed control does all the work.
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If you are interested in finding one of the speed controls they are easy to find for reasonable prices on ebay. I use mine ALL THE TIME!