crochet rug help

Hello, I am making a crochet rug from old sheets. I have made a large circle and would like to add large half circles to it. I tried making a half circle, but they don't fit well, so I have started to make my half circle directly attached to the large circle. however, I'm new to crocheting, and am experiencing a bit of difficulty to increase, continue and decrease to make the half circle the size of half of the large circle but attached. can anyone help? thanks, Nicole