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数学 高校生

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9/18X 本 例題 87 接弦定理を用いた証明問題 図のように、大きい円に小さい円が点Tで接してい 点Sで小さい円に接する接線と大きい円との交 A,Bとするとき、∠ATSとBTSが等しい る。 00000 ことを証明せよ。 B 240Q 基本事項 2 CHART & THINKING 接線と弦には 接弦定理 [神戸女学院大 ] B p.394 基本事項 2 399 点Tにおける2つの円の接線と, 補助線 SP (Pは線分AT と小さい円との交点) を引き, 接 弦定理を利用する。 接弦定理を用いて, 結論にある ∠ATS や ∠BTS と等しい角にどんど ん印をつけていき,三角形の角の和の性質に関連付けて証明することを目指そう。 3章 10 答 点Tにおける接線を引き、図のよう C. に点Cを定める。 ■弧に対す しい。 また、線分AT と小さい円との交点 をPとし, 点Sと点Pを結ぶ。 P BC 接点Tに対して,接線 TC は小さい 円,大きい円の共通接線であるから ZATC=TSP-TBS A BA B ← 2円が接する→2円 の共通接線が引ける。 と接線 接弦定理 接点Sに対して, 接線 AB は小さい円の接線であるから ∠ASP = ∠ATS ② ◆接弦定理 ◆接弦定理 (三角形の外角)=(他の 2つの内角の和) ・③ m TBS △TSB において <BTS + <TBS = ∠AST と接線 ここで KAST = ∠ASP + ∠TSP 弦定理 ww って wwwww ①③から <BTS + ∠TBS= ∠ASP + ∠TSP <BTS = ∠ASP ゆえに、②から <BTS = ∠ATS PRACTICE 87 8 右の図のように,円に内接する △ABC と Aにおける接線 がある。 ただし, AC <BC とする。 辺BC上にAD=BD 分 となるように点Dをとり, 線分ADの延長と円0の交点をE, D レキ △ABC B 円と直線、2つの円

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英語 中学生

これの答えがないためだれか答えを教えてください‼️‼️よろしくお願いします🙇🏻‍♀️‪💧

[B] The Threat of Tourism As air travel gets cheaper, more and more people are visiting famous sites around the world. Although this increase in tourism brings economic benefits to the areas around these sites, tourists also cause unexpected problems. In particular, some famous works of art are being affected. This is because people's breath increases carbon dioxide and humidity levels. Gradually, these levels damage, old paintings and other works of art. One famous site facing this problem is the Sistine Chapel in the Vatican in Rome. The 500-year-old paintings, especially the famous ceiling by Michelangelo, are so popular that as many as 2,000 people may be viewing them at a time. In 1994, after noticing that the visitors' breath was damaging the paintings, the Vatican purchased an expensive air-conditioning system to protect them. However, the crowds continued to increase, so in 2014, the Vatican decided to limit the number of visitors to about 6 million a year. Another site that faces a similar problem is the Mogao Caves in Dunhuang, China. These caves are full of beautiful Buddhist paintings and sculptures that attract thousands of visitors every year. Many of the artworks are very old and, as with the Sistine Chapel, the carbon dioxide in the breath of visitors is gradually damaging them. Originally, 40 of the 400 caves were open to visitors, but this number was reduced by half in 2014. In addition, the number of visitors allowed into the caves has been greatly reduced. A different solution is being tried in the Ajanta Caves in Maharashtra, India. The caves also have many ancient Buddhist paintings in them, and these too are being damaged. In order to protect the paintings, visitors are quickly rushed through the caves. However, many visitors complained about the short time, saying they could not look at the paintings properly, so the local government built a visitors' center with exact copies of the caves. Visitors are allowed to study these copies for as long as they like. The local government hopes this will provide a good balance between protecting the paintings and giving tourists a good experience. (30) As the number of tourists increases, 1 unexpected economic problems occur among people living around famous sites. 2 the carbon dioxide and humidity in their breath harm the things they go to see. 3 air pollution caused by the carbon dioxide from airplanes increases. 4 people have trouble breathing because of the high levels of humidity. (31) In 1994, the Vatican 1 allowed only 2,000 tourists to look at its paintings by Michelangelo. 2 invited 6 million visitors to see its 500-year-old wall paintings on one day. 3 installed an air-conditioning system in order to make visitors more comfortable. 4 tried to reduce damage to its paintings by buying an air- conditioning system. (32) What is one thing that has been done to protect the Buddhist artworks in Dunhuang? 1 More of the Mogao Caves have been closed to visitors. 2016年度第2回 新試験 2 Visitors are being asked to avoid breathing too close to the paintings. 3 Some of the visitors are being taught new ways to preserve paintings. 4 The number of visitors has been reduced from 400 to 40 a day. (33) Why were some visitors to the Ajanta Caves unhappy? 1 The majority of the paintings have turned out to be copies. 2 There were not as many Buddhist paintings as they had expected to see. 3 They did not have enough time to look at the paintings inside the caves. 4 The long lines at the visitors' center have prevented them from seeing the paintings. 29

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