Picture: http://postimg.org/image/mm0x8zwmh/
In the figure, TA and TB are tangents to the circle. Find the unknowns.
I use method 1 to find:
Picture of method 1: http://postimg.org/image/xa4o7u6ll/
But the answer of y is incorrect.
Then I use method 2 to find. That is finding out angle ODC=24°, then use ∠ in alt. segment to find y and the answer is correct.
I want to know why method 1 is wrong. Thank you!~
F.5 maths circle(3)
2014-12-26 8:46 am
回答 (2)
2014-12-27 6:17 pm
✔ 最佳答案
If O is the centre, then the question is wrong. So you can get many solutions.Given : ∠OCD＝24°, ∠OCT＝30°, ∠ODT＝38°.
Join OT, so OC＝OD＝OT＝radius,∠ODC＝∠OCD＝24°,∠OTC＝∠OCT＝30°,∠OTD＝∠ODT＝38°,angle sum of △CDT＝24°＋30°＋38°＋24°＋30°＋38°＝184° ≠ 180°
So, this is a wrong question. I think the purpose of this question is want you to know how to use the reason 'angle in alternate segments'. So,x＝∠OCD＋∠OCT＝24°＋30°＝54° ⋯⋯ (∠s in alt. seg.)y＝∠ODC＋∠ODT＝24°＋38°＝62° ⋯⋯ (∠s in alt. seg.)
2014-12-26 9:36 am
因為題目比多左隻角
如果∠OCT=30° 而∠OCD=24°
咁∠DOT=2(30°+24°)=108° (∠ at centre twice ∠ at circumference)
∠ODT=∠OTD (base ∠, isos tri)
∠ODT=(180°-108°)/2=36°
咁∠ODT就唔應該係38°
所以呢題其實唔洗比番3隻角出黎
btw, 係呢題到 y 仲可以係58° 0.0
2014-12-26 02:27:36 補充：
OT=OC=OD (radii)
∠OTC=∠OCT=30° (base ∠, isos tri)
∠OTD=∠ODT=38° (base ∠, isos tri)
∠CTD=30°+38°=68°
x=30°+24°=54° (∠ in alt segment)
y=180°-54°-68°=58° (∠ sum of tri)
如果∠OCT=30° 而∠OCD=24°
咁∠DOT=2(30°+24°)=108° (∠ at centre twice ∠ at circumference)
∠ODT=∠OTD (base ∠, isos tri)
∠ODT=(180°-108°)/2=36°
咁∠ODT就唔應該係38°
所以呢題其實唔洗比番3隻角出黎
btw, 係呢題到 y 仲可以係58° 0.0
2014-12-26 02:27:36 補充：
OT=OC=OD (radii)
∠OTC=∠OCT=30° (base ∠, isos tri)
∠OTD=∠ODT=38° (base ∠, isos tri)
∠CTD=30°+38°=68°
x=30°+24°=54° (∠ in alt segment)
y=180°-54°-68°=58° (∠ sum of tri)
收錄日期: 2021-04-15 17:39:40
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20141226000051KK00004