circle(2)
2011-06-11 5:14 pm
圖片參考：http://img827.imageshack.us/img827/2849/58119271.jpg
In the figure, ABCD is a circle. IF arcAB：arcBC：arcCD：arcDA=1：2：3：3 and E is a point lying on BD, then angleCAE=?
回答 (1)
2011-06-11 5:34 pm
✔ 最佳答案
Join AD and CD. Then let O be the centre of the circle. We have:Suppose ∠ADB = x, then
∠CDB = 2x, ∠DAC = 3x and ∠DCA = 3x (arc ratio = angle ratio)
∠ABO = 2∠ADB = 2x, ∠COB = 2∠CDB = 4x, ∠COD = 2∠DCA = 6x and ∠DOA = 2∠DCA = 6x (∠ at centre = twice ∠ at circumference)
So 2x + 4x + 6x + 6x = 360, givine x = 20
Hence ∠ADB = 20 and ∠DAC = 60
.∠AEB = ∠DAE + ∠ADB (Ext. ∠ of triangle), giving ∠DAE = 10
∠CAE = ∠DAC - ∠DAE = 50
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