IN THE FOLLOWING FIGURES, O is the centre.
15. In the figure, ABCD is a cyclic quadrilateral. Chords AB and DE intersect at G. CBF is a straight line. IF arc CBE = arc AE, prove that BE bisects angle ABF.
圖片參考：http://imgcld.yimg.com/8/n/HA00610265/o/701010110121913873376890.jpg
MATH QUESTION CIRCLES 3
2010-10-12 4:32 am
回答 (1)
2010-10-12 4:48 am
✔ 最佳答案
Since arc CBE = arc AE ,ㄥADE = ㄥCDE (equal arcs, equal ∠s)ㄥADE = ㄥABE (equal chords, equal ∠s)Let ㄥADE = ㄥCDE = ㄥABE = K degrees.On the other hand , ㄥADC = ㄥABF (ext. ∠s, cyclic quad.)i.e.ㄥADE + ㄥCDE = ㄥABE + ㄥFBEK + K = K + ㄥFBEㄥFBE = Ki.e. ㄥFBE = ㄥABE , therefore BE bisects angle ABF.
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