题目

Brenda Bongos was a happy, artistic girl. She had one big dream—to play the drums in a band. But one big problem lay in her way. To be good enough to play in a band, Brenda had to practice a lot, but she lived next-door to a lot of old people. Many of them are sick. She knew that the sound of beating drums would really get on their nerves. So, she had tried playing in the strangest places: a basement, a kitchen, and even in a shower. But there was always someone it would annoy.     One day, while watching a science documentary on TV, she heard that sound cannot travel in space, bec如图所示，⊙I是Rt△ABC（∠C=90°）的内切圆，⊙I和三边分别切于点D，E，F．（1）求证：四边形IDCE是正方形；（2）设BC=a，AC=b，AB=C，求内切圆I的半径．