258－58－26－74

    There are three people in Yang Yang's family. They like different kinds of food. Yang Yang likes rice a lot. But she doesn't like chicken at all. Her father is from Shanxi. He doesn't like rice at all. He likes chicken and bread very much. Her mother is from Dalian. She doesn't like rice or bread at all. But she likes fish and vegetables a lot. They love each other and help each other.

如图，在平面直角坐标系中，点A坐标为（6，0），在B在y轴的正半轴上，且S_△AOB=24．

（1）求点B坐标；

（2）若点P从B出发沿y轴负半轴运动，速度每秒2个单位，运动时间t秒，△AOP的面积为S，求S与t的关系式，并直接写出t的取值范围；

（3）在（2）的条件下，若S_△AOP：S_△ABP=1：3，且S_△AOP+S_△ABP=S_△AOB，在线段AB的垂直平分线上是否存在点Q，使得△AOQ的面积与△BPQ的面积相等？若存在，求出Q点坐标；若不存在，请说明理由．

已知：如图，在△ABC中，AB=AC．

（1）尺规作图：作∠BAC的角平分线AD，交BC于点D．（不要求写作法，保留作图痕迹）

（2）延长AD至E点，使DE=AD，连接BE、CE．求证：四边形ABEC是菱形．