AB//CD and they are 4cm apart.Pand Q are the mid-points of AB and CD respectively.If AB = 16cm and CD=12cm ,PQ=4cm find
a. the length of OP
b. the radius of the circle
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F.4 Maths
2007-10-30 5:03 am
回答 (2)
2007-10-30 5:16 am
✔ 最佳答案
a)OP = x
(radius)^2 = 64 + x^2 = 36 + (4 + x)^2
64 + x^2 = 36 + 16 + 8x + x^2
8x = 12
x = 3/2
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b)
(radius)^2 = 64 + (3/2)^2
radius = sqrt(265)/2
2007-10-29 21:17:28 補充：
死火, 慢左, 不過我做得都簡單快手, 投我一票, 唔該
2007-10-30 5:14 am
(a) As P and Q are respectively the mid-points of AB and CD, OQ is perpendicular to CD and OP is perpendicular to AB.
In triangle OAP, (16/2)^2 + (OP^2) = OA^2
64+OP^2 = OA^2
In triangle OQC, (12/2)^2 + (4+OP)^2 = OC^2
36+16+8OP+OP^2 = OC^2
Since OA = OC = radius, 36+16+8OP+OP^2 =64+OP^2
8OP = 12
OP = 3/2 cm = 1.5 cm
(b) Radius = sqrt(8^2 + 1.5^2) = sqrt(66.25) = 8.1394 cm (4 d.p.)
In triangle OAP, (16/2)^2 + (OP^2) = OA^2
64+OP^2 = OA^2
In triangle OQC, (12/2)^2 + (4+OP)^2 = OC^2
36+16+8OP+OP^2 = OC^2
Since OA = OC = radius, 36+16+8OP+OP^2 =64+OP^2
8OP = 12
OP = 3/2 cm = 1.5 cm
(b) Radius = sqrt(8^2 + 1.5^2) = sqrt(66.25) = 8.1394 cm (4 d.p.)
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071029000051KK03843