標題:
F.5 maths circle(3)
發問:
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... 顯示更多 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!~ 更新: RE YA HOO ! 知識+管理員： 可唔可以講吓y=58° 嘅計法？囧
最佳解答:
其他解答:
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)
F.5 maths circle(3)
發問:
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... 顯示更多 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!~ 更新: RE YA HOO ! 知識+管理員： 可唔可以講吓y=58° 嘅計法？囧
最佳解答:
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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.)其他解答:
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)
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