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2008-03-21 5:58 pm

The figure shows sector OABCD. arcAB:arcBC:arcCD=1:3:5. AC and BD intersect at P.
(a) Find angle AOB and angle BOC
(b)Find angle OAD
(c)Fing angle CAD

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更新1:

可否詳細地列出步驟,plz~

回答 (1)

Chui Ling

2008-03-21 8:52 pm

✔ 最佳答案

I think you miss something, such as the angle AOD
so here I assume the angle AOD to be 9a

a. then we can get angle AOB = a (arcs prop.to angles at centre)
angle BOC = 3a (arcs prop.to angles at centre)

b. obviously triangle OAD is a isos. triangle
angle OAD = angle ODA (base angles, isos. triangle)
angle OAD = (180-9a)/2 (angles sum of triangle)

c. angle CAD = 1/2 angle COD (angle at centre twice angle at circumference)
angle COD = 5a (arcs prop.to angles at centre)
so angle CAD = (5/2) a

Hope can help you

參考: myself

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