Quadrilateral

2009-04-24 7:21 pm
OABC is a quadrilateral (O is the origin and counting anti-clockwise). AB = 15, BC = 9 and OC = 10. Angle COA = 80 degree, angle OAB = 30 degree. Find length of OA and angle ABC. (correct to 3 sig. fig.)
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Can 002 please show the steps, thanks. Without this, it is difficult to offer you the points. Please help.

回答 (3)

2009-04-25 9:27 am
✔ 最佳答案
The answer is as follows:

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2009-04-24 9:21 pm
OA = 23.4 (correct to 3 sig. fig.)

angle ABC = 165 degree (correct to 3 sig. fig.)
2009-04-24 8:09 pm
since OABC is a quadrilateral and O is the origin

then OA = OC = radius = 10

let E be a point on the arc AC

angle AEC = 1/2 angle COA =40 degree
(angle at center=2 angle at circumference)

angle AEC + angle ABC = 180 degree (圓內接四邊形對角互補)
angle ABC= 180-40 =140 degree


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