已知∠AOB=90°，OM是∠AOB的平分线，按以下要求解答问题：
（1）如图1，将三角板的直角顶点P在射线OM上移动，两直角边分别与OA,OB交于点C，D．

①比较大小：PC______PD． (选择“>”或“<”或“=”填空）；
②证明①中的结论．
（2）将三角板的直角顶点P在射线ＯＭ上移动，一直角边与边OA交于点C，且OC=1，另一直角边与直线OB，直线OA分别交于点D，E，当以P，C，E为顶点的三角形与△OCD相似时，试求OP的长．（提示：请先在备用图中画出相应的图形，再求OP的长）.

阅读理解

　　Lang Lang is a famous Chinese pianist. He was born in 1982 in Shenyang. He showed his talent(天赋)for playing the piano when he was two. He began to take piano lessons at the age of 3. At the age of 5, he won the Shenyang Piano Competition. When he was 11, he won the first prize at the Fourth International Young Pianists Competition.

    He began his study at Curtis Institute(学院)in America when he was 15. He became the first Chinese student at the institute. During his study there he made great progress and became a top pianist. On August 14th, 1999, the great Andre Watts was ill so Lang Lang played at concert instead of him and he was successful. Then he became famous all over the world.

    In August of 2008, more than 5 billion people watched Lang Lang's performance at the opening ceremony(开幕式)of the Beijing Olympic Games. He also played at the opening ceremony of the Shanghai Expo(世博会).

    Years ago, I lived in a building in a large city. The building next door was only a few feet away from mine. There was a woman who lived there, whom I had never met, yet I could see her seated by her window each afternoon, sewing or reading.

    After several months went by, I began to notice that her window was dirty. Everything was unclear through the dirty window. I often said to myself, "I wonder why that woman doesn't wash her window. It really looks terrible."

    One bright morning I decided to clean my flat, including washing the window on the inside.

    Late in the afternoon when I finished the cleaning, I sat down by the window with a cup of coffee for a rest. What a surprise! Across the way, the woman sitting by her window was clearly seen. Her window was clean!

    Then it dawned on me. I was always criticizing(批评) her dirty window, but all the time I was watching hers through my own dirty window.

    That was quite an important lesson for me. How often had I looked at and criticized others through the dirty window of my heart, through my own mistake?

    Since then, whenever I wanted to judge(评判) someone, I asked myself first, "Am I looking at him through my own dirty window?"

    Then I try to clean the window of my own world so that I may see the world around me more clearly and correctly.

设双曲线  $\frac{y^2}{a^2}-\frac{x^2}{3}=1$的两个焦点分别为F₁、F₂离心率e=2.