標題:

F.4MATHSx1

發問:

1.In the figure,OABC is a parallelogram. website of figure: http://hk.myblog.yahoo.com/rain_021624/photo?pid=1&fid=2 a)Is OABC a rhombus?Briefly explain your answer. b)Prove that 角ABC = 180度- x/2. c)Hence,find x.

最佳解答:

a) OC = OA (radius of circle) OC = AB ( side of parallelogram) therefore OA = AB. Similarly, OA = BC ( side of parallelogram). Therefore, OC = OA = AB = BC, that means OABC is a rhombus. b) Reflex angle ADC = 360 - x. Therefore, angle ABC = half of reflex angle ADC = (360 - x)/2 = 180 - x/2 ( angle at circumference is half angle at centre). c) Since OABC is a parallelogram, opposite angles are equal, therefore, x = 180 - x/2 3x/2 = 180 x = 360/3 = 120 degree.

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