MATH QUESTIONS [CIRCLES]

[匿名]

2010-09-23 1:46 am

16. In the figure, AEC and BED are straight lines. Given that angle BAD = 86, angle CBD = 46 and angle CDB =40, prove that ABCD is a cyclic quadrilateral.

圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701009220077713873372920.jpg

17. In the figure, C and F are points on BD and AB respectively such that angle BAC = 40 and angle BDF = 30. Given that AC intersect DF at E and angle AFD = 85.

a) find angle BCE.
b) prove that BCEF is a cyclic quadrilateral.

圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701009220077713873372921.jpg

回答 (1)

用戶2053

2010-09-23 3:53 am

✔ 最佳答案

16)ㄥBCD = 180 - 46 - 40 = 94°ㄥBCD + ㄥBAD = 94 + 86 = 180° So ABCD is a cyclic quadrilateral.(opp. ∠s, cyclic quad.) 17a)ㄥAEF = 180 - 85 - 40 = 55° = ㄥCED (vert. opp. ∠s) ㄥBCE = ㄥEDC + ㄥCED = 30 + 55 = 85° (ext. ∠ of Δ .)b)ㄥBCE = ㄥAFD = 85°So BCEF is a cyclic quadrilateral. (ext.∠= int. opp.∠)

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