题目

Dear Tom, How is it going? My family and I are exciting to hear that you will come to China to spend the Chinese New Year’s Eve. And I am glad to tell you the arrangements during your visit in advance. I will meet you at 4 o’clock in the afternoon of February 18th. I can arrive at the northwestern entrance of Zhongguancun Station of Subway Line 4. If you have some trouble finding the right way, you can seek help from the subway staff and ring me up directly. After you arrived, we will have various traditional activity, such as watching the Spring Festival Gala, making dumplings, and如图，已知直径与等边△ABC的高相等的圆O分别与边AB、BC相切于点D、E，边AC过圆心O与圆O相交于点F、G．（1）求证：DE∥AC；（2）若△ABC的边长为a，求△ECG的面积．