maths question

[匿名]

2012-07-30 4:14 am

圖片參考：http://imgcld.yimg.com/8/n/HA00517423/o/701207290052413873413280.jpg

in the figure,o is the centre of the circle.AC and BD are chords intersecting at E such that BE=CE.

1.SHOW THAT A,E ,O AND B ARE CONCYCLIC.
2.IF ANGLE OEB=56 DEGREE, FIND ANGLE AEB AND ANGLE ODC.

ANSWER:ANGLE AEB=68 DEGREE, ANGLE ODC=56 DEGREE

回答 (1)

用戶2053

2012-08-05 1:35 am

✔ 最佳答案

1)
∠CAB = (1/2)∠COB (∠at centre twice ∠ at ☉ce)
Let M be the mid point of BC , then OM ⊥ BC and EM ⊥ BC since EM is the height of isos.△ BEC , so EOM is a straight line
So ∠BOM = (1/2)∠COB =∠CAB ,
therefore A,E ,O AND B ARE CONCYCLIC. (ext.∠= int. opp.∠)
2)
∠EBC =∠ECB = 90° - ∠OEB = 90 - 56 = 34°
so∠AEB = ∠EBC + ∠ECB = 34° + 34°= 68° (ext. ∠ of Δ)∠ODC
= (180° - ∠DOC)/2
= (180° - 2∠EBC )/2 (∠at centre twice ∠ at ☉ce)
= (180° - 2*34° )/2
= 56°

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