Circle properties (5m)

用戶90882

2010-07-25 7:07 pm

Can you help me to do this question? Thank you. 5 marks
Please show steps.

Link: http://www.sendspace.com/file/dzsfcf

From New Trend Senior Secondary Mathematics S5A Ch.2 Revision exercise 2 #23

回答 (1)

用戶10012

2010-07-25 7:41 pm

✔ 最佳答案

Since arc PS = arc QR, so angle SQP = angle QSR (equal arc equal angle).
Therefore, triangle SQX is an isos. triangle.
Angle QXR = angle SQP + angle QSR (ext. angle of triangle) = 2 angle SQP = 2 angle SQX.
(b)Angle SXP = angle QXR ( vert. oppo. angle)...........(1)
Angle SOP = 2 angle SQX ( angle at centre twice angle at circumference)
= angle QXR (from result of (a))...........(2)
From (1) and (2), angle SXP = angle SOP
therefore P,S,O,X are concyclic ( angle in same segment equal).

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