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[Maths] Math 2005-Paper I-17

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Math 2005-Paper I-17

How to do part (bii)?
Thanks
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(b)(ii)The radius=MN/2
        Centre:The circle intersects x-axis at two point.
                   Apart from the origin, plz concerntrate on the other point.(Let X be the point)
                   XR is a diameter.
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but why is the y-coordinate of the centre is 1/2 of OR??
that means MN//PQ??

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回覆 #3 Avrence 的帖子

the y-coordinate of the centre "is not" 1/2 of OR
You should consider X and R
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but that's what written in the marking...
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回覆 #5 Avrence 的帖子

雖然我都計到呢個answer,但係OR/2我都未係好明..
AL2012..加油啊!

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我知啦!因為OR係一條垂直於x軸既chord,所以line from center bissects chord perpendicular to chord,then OR/2=y-coordinate of the centre
AL2012..加油啊!

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yea, i dont understand this method too
so can you post out your method?

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回覆 #8 Avrence 的帖子

I have understood it.
Line from centre perpendicular to chord bisects chord.
---------------------------------my method--------------------------------------------
b(ii)OM/RP=ON/RQ
     .......
     OM^2=13

     MN^2=ON^2+OM^2
    .......
     MN=13/2
     radius=13/4

     Let X be the intesecrtion point of the circle and the x-aixs other than the origin.
    XR=diameter=MN=13/2
    XR^2=OR^2+OX^2
    ........
    OX=5/2
     The coordinates of X are(-5/2,0)

     The x-coordinate of the center=(-5/2+0)/2=-5/4
    The y-coordinate of the center=(6+0)/2=3
     Therefore,(-5/4,3)
AL2012..加油啊!

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If you really don't understand the marking scheme,
do the following step.

1.draw the center of the circle
2.draw the mid-point of OR
3.connect them
You may realize that"Line from centre perpendicular to chord bisects chord."
AL2012..加油啊!

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