①四边形 $EGFH$ 一定是菱形；② $AC//$ 平面 $EGFH$ ；③四边形 $EGFH$ 的面积 $S=f\left(x\right)$ 在区间 $0,1$ 上具有单调性；④四棱锥 $A-EGFH$ 的体积为定值.

以上结论正确的个数是（   ）

如图，BE是圆O的直径，A在EB的延长线上，AP为圆O的切线，P为切点，弦PD垂直于BE于点C．

（1）求证：∠AOD=∠APC；

（2）若OC：CB=1：2，AB=6，求圆O的半径及tan∠APB．

根据短文理解，从A、B、C、D四个选项中选择最佳答案填空。

    One day, when Bill was walking home from school, he heard a 1 coming from the bushes(灌木). He went over  2 what it was. Behind a bush, he found a black dog. Bill went back home as soon as he could with the dog and 3 her to his parents. Bill's dad found that the dog had 4 leg, so they brought the dog to a doctor for animals 5 car. On the way Bill's parents decided that Bill could 6 the dog if they couldn't find the owner of the dog.

     When they arrived, the doctor checked the dog. He told Bill that she was going to have 7! The next day, Bill 8 signs like "FOUND DOG BACK" around his neighborhood. He also wrote his family's phone number on the signs.

     Two days later, Bill got a/an 9 from the owner of the dog. The owner thanked Bill. When he came to pick up his dog, he said Bill could have one of the babies. Bill was very 10! Finally Bill got a baby dog from the owner. He named him Rosco and liked him very much.