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选做题 (几何证明选讲选做题)如图,AB是半圆O的直径,点C在半圆上,CD⊥AB于点D,且AD=3DB,设∠COD=θ,则tan2=____________. 答案：  设圆O的半径为R,由图可得OD=R·cosθ,∴AD=R+R·cosθ,DB=R-R·cosθ.∴R+Rcosθ=3(R-R·cosθ).∴cosθ=,θ=60°.∴tan2=tan230°=.The Friday after the American holiday of Thanksgiving is called Black Friday. It’s said that it’s the day that store ledgers(分类账)move into the black and companies become profitable（有利可图的，有益的）. On that day, retailers（零售商）slash prices to get consumers to buy.  It is also a time when many Americans start their Christmas shopping. VOA’s Elizabeth Lee tells us how the economy may affect consumers on that bargain day.  “It’s just the deals, the sales and everything you can get for a lesser（较少的，较小的）price,” said Sandy Thomas, a shopper. But it’s a nightmare（噩梦）for others. “I think it’s crazy. I’ve done all of my shopping throughout the week so I don’t have to go out on Friday,” she said. It’s called Black Friday, the start of the traditional Christmas shopping season in the United States. Every year it’s the day after the Thanksgiving holiday. Stores open before sunrise and there are deep discounts everywhere you look. While the lead up to Christmas is known as the season of giving, Black Friday can get ugly. Last year a crowd of bargain-hunters killed a Wal-mart（沃尔玛公司）worker in a New York suburb. This year, many stores are increasing security while they slash prices. “This is a huge time for the retail stores,” said Fred Joutz from George Washington University. “This is when they begin making their profits for the year.” Economics professor Fred Joutz says how Americans spend the weekend after Thanksgiving is a good indication of how consumers feel about the future. With the unemployment rate above 10 percent, Joutz says Americans are saving more and spending less. “Credit is still strictly controlled whether through credit cards or through borrowing from banks,” he said. Some retailers are attracting consumers by opening on Thanksgiving Day, when shops are traditionally closed.  Other stores open their doors anywhere from midnight to four in the morning. And shoppers will be lining up in front of the doors in order to be one of the first ones to walk through and get a big discount. Electronics like flat screen TVs are usually the first items to go. Sandy Thomas says it’s an annual family tradition and well worth it. “I just save maybe half of what I would have spent on a regular, you know, shopping trip,” she said. Economists say U.S. consumers will spend money this Black Friday, but they will spend it more carefully.      1. The underlined word “slash” in the first paragraph probably means _________.  A. reduce         B. raise         C. increase        D. change 2.The sentence “This day should be a shopper’s dream.” should be placed between ________.  A. paragraph two and paragraph three        B. paragraph one and paragraph two  C. paragraph three and paragraph four      D. paragraph five and paragraph six 3.Why are many stores increasing security according to the passage?  A. Because there are too many people saving more and spending less.  B. Because it’s a time when they begin making their profits for the year.  C. Because last year a crowd of bargain-hunters caused an accident.  D. Because many stores open their doors from midnight to four a.m. 4.What can we learn from the passage?  A. Christmas shopping is traditional time and this year it is no exception.  B. Electronics like flat screen TVs are usually least discounted.  C. The economy only affects consumers on that bargain day.  D. Thanksgiving is a good indication of how consumers feel about the future.