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標題: Tagents to Circles [打印本頁]

作者: jyuenws    時間: 2011-5-16 10:11 PM     標題: Tagents to Circles

唔好意思丫, 又係我丫 我又唔識計啦....

Q21.  我畫到張紙花哂都唔識點prove


Q24.  我試過join 咗 zy 同 zx, 跟住搵angle 搵咗n 耐, 結果都係唔識搵 xy 既length.   答案係..... 3 cm


Q36.a) 我唔係好識prove 野.....

b) 好亂丫

sorry ar, 我知我蠢, 但大家幫下我啦, 聽日test 啦 唔該哂!
作者: Simon    時間: 2011-5-16 10:27 PM

Q21. Prove that angle OCD is a right angle.
  Proof: Consider the angle sum of triangle OCD
  (Hints: total 4 reasons to prove)

Q24. No need to join any lines.
  Use the properties of tangents, and cosine law to find the length of XY.

打住先...
作者: 11AL考生    時間: 2011-5-17 12:08 AM

21) angle BOA = 60 (angle at centre = twice angle at circumference)
=> angle BFO = 90
=>angle OCD =90

24)
[attach]33871[/attach]
作者: Simon    時間: 2011-5-17 12:34 AM

Q36
a. Construct a line from S to a point on OX such that the line is perpendicular to OX
 Then you can solve it by Pyth. Thm.
b. First, find CA, CB and BA respectively with aid of part a
 Then use the fact that CA = CB + BA
作者: 11AL考生    時間: 2011-5-17 12:43 AM

引用:
原帖由 Simon 於 2011-5-17 12:34 AM 發表
Q36
a. Construct a line from S to a point on OX such that the line is perpendicular to OX
 Then you can solve it by Pyth. Thm.
b. First, find CA, CB and BA respectively with aid of part a
 Then  ...
alternative method
得閒得制既方法
[attach]33872[/attach]

[ 本帖最後由 11AL考生 於 2011-5-17 12:55 AM 編輯 ]
作者: 11AL考生    時間: 2011-5-17 12:50 AM

by a)

作者: Simon    時間: 2011-5-17 12:54 AM

[attach]33873[/attach]
Part a:
OT = x, ST = y (radii)
OS = x + y
OM = x - y
MS[suptag]2[/suptag] = OS[suptag]2[/suptag] - OM[suptag]2[/suptag]
= x^2 + 2xy + y^2 - x^2 + 2xy - y^2
= 4xy
MS = 2 sqrt(xy)
XY = MS = 2 sqrt(xy)

Part b:
By part a, we have
AB = 2 sqrt(ab)
BC = 2 sqrt(bc)
AC = 2 sqrt(ac)

CA = CB + BA
sqrt(ca) = sqrt(cb) + sqrt(ba)
Divide both sides by sqrt(abc)
1 / sqrt(b) = 1 / sqrt(a) + 1 / sqrt(c)
作者: jyuenws    時間: 2011-5-17 01:45 AM

唔該哂兩位




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