F4 math problems ( Circles )

2007-03-31 12:57 am

In the figure, EA = AB = BC and ∠ABE = 48°.
(a) Find ∠BCD.
(b) Find ∠CDE.

Figure http://server5.pictiger.com/img/1022171/picture-hosting/2.jpg

回答 (1)

chaoseng2000

2007-03-31 7:13 am

✔ 最佳答案

在此題中你可先求弧的度數
∵∠ABE = 48°,
即弧AE=96°,(圓周角所夾的弧的度數等於此圓周角的度數的兩倍)
又∵EA = AB = BC
∴弧EA = 弧AB = 弧BC =96° (在同圓中,等弧夾等弧)
弧CE=360°-3*96° = 72°
(a)
∵點D沒有足夠條件限制,
即D可在弧CE上任意一點
0° < 弧DE < 弧CE = 72°
∠BCD的度數=(弧AB +弧EA +弧DE )/2的度數=96° + 弧DE/2的度數
∴96° + 0° < ∠BCD < 96° + 36°
96° < ∠BCD < 132°

(b)
∠CDE的度數 = (弧EA + 弧AB + 弧BC)/2的度數 =144°

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