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托勒密定理

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托勒密定理 - PowerPoint PPT Presentation


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托勒密定理. ( 兩條對角線乘積 = 兩雙對邊乘積之和 ). 商高定理 和差角公式 餘弦定理. 某些時候 半徑趨近 推廣. 托勒密定理. 任意凸四邊形. Euler 定理. 當圓內接四邊形為 矩形 時. ( 商高定理 ). 當圓內接四邊形為 等腰梯形 時. ( 餘弦定理 ). 有一邊為直徑 (=1) 時. ( 正弦和角公式 ). 有一邊為直徑 (=1) 時. ( 正弦差角公式 ). 推廣的托勒密定理. 設 ABCD 為平面上任意 凸四邊形 ,則. ,當 ABCD 四點共圓等號成立.

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Presentation Transcript
slide2

托勒密定理

(兩條對角線乘積=兩雙對邊乘積之和)

slide3

商高定理

和差角公式

餘弦定理

某些時候

半徑趨近推廣

托勒密定理

任意凸四邊形

Euler定理

slide6
有一邊為直徑(=1)時

(正弦和角公式)

slide7
有一邊為直徑(=1)時

(正弦差角公式)

slide8
推廣的托勒密定理

設ABCD為平面上任意凸四邊形,則

,當ABCD四點共圓等號成立

euler
Euler定理

設A,B,C,D為直線上按序的四點,則

【證明】

slide12

報告完畢

謝謝聆聽!