题目

阅读短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。 Stephen Hawking is perhaps the world's most famous living physicist. To the public, he's best known as an author of bestsellers such as The Universe in a Nutshell and A Brief History of Time, which have brought an appreciation of theoretical (理论上的) physics to millions. He is regarded as having one of the brightest minds on the planet. But outstanding astrophysicist (天体物理学家) Stephen Hawking has admitted that he did not learn to read until he was eight years old.In a public lecture at 已知Rt△ABC中，∠ACB=90°，CA=CB，有一个圆心角为45°，半径长等于CA的扇形CEF绕点C旋转，直线CE、CF分别与直线AB交于点M、N．（1）如图①，当AM=BN时，将△ACM沿CM折叠，点A落在弧EF的中点P处，再将△BCN沿CN折叠，点B也恰好落在点P处，此时，PM=AM，PN=BN，△PMN的形状是　 　．线段AM、BN、MN之间的数量关系是 　；（2）如图②，当扇形CEF绕点C在∠ACB内部旋转时，线段MN、AM、BN之间的数量关系是　 　．试证明你的猜想；（3）当扇形CEF绕点C旋转至图③的位置时，线段MN、AM、BN之间的数量关系是　 　．（不要求证明）