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Another way of answering the cirle geometry question (1 Viewer)

J2good4u

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I sat my HSC last year but looking at this question would this be valid:

let angle QBA = x
therfore angle BAP = x (alternate angles in parallel lines...)
Similarly, let angle BQP = y
therfore angle APQ = y (alternate angles in parallel lines...)

Now, angle QTA = x + y ( the exterior triangle BQT is equal to the sum of the opposite interior angles)
Also, angle ATP = 180 - (x + y) ( angle sum of triangle PAT 180)

Therefore angle QTP = x + y + 180 - (x +y)
= 180

Thus Q,T,P are collinear
 

SpiralFlex

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Didn't you just post this on the circle geom thread?
 

J2good4u

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Yes, but I posted it on a thread to get a direct answer...Well?
 

SpiralFlex

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I sat my HSC last year but looking at this question would this be valid:

let angle QBA = x
therfore angle BAP = x (alternate angles in parallel lines...)
Similarly, let angle BQP = y
therfore angle APQ = y (alternate angles in parallel lines...)


Now, angle QTA = x + y ( the exterior triangle BQT is equal to the sum of the opposite interior angles)
Also, angle ATP = 180 - (x + y) ( angle sum of triangle PAT 180)

Therefore angle QTP = x + y + 180 - (x +y)
= 180

Thus Q,T,P are collinear
This line is not valid. Therefore the lines below are not valid. :)
.
 
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At most 1. I think in past papers and trials they usually give 1 mark for being on the correct path to the solution but not sure about this situation
 

panda15

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is this a zero out of three? I did this aswell unfortunately, wasn't thinking straight
Maybe 1 mark. Depends on how many people got the correct solution as to whether they award a mark for the first part.
 

aDimitri

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i would guess it's a 0/3 since literally none of this proof is used in the actual valid method (i.e. constructing a tangent).
 

liuque

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I did the similar thing.
yet the parallel lines are not used +_+
Link QT and PT
ATQ is the external angle of the triangle ATP
therefore ATQ=APT+TAP (exterior angle is the sum of the opposite angles)
yet the angle ATP=180-(APT+TAP)
therefore ATP=180-ATQ
i.e. ATQ+ATP=180
Q,T,Pare collinear

anyone knows if this is legit ?
 

RealiseNothing

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I did the similar thing.
yet the parallel lines are not used +_+
Link QT and PT
ATQ is the external angle of the triangle ATP
therefore ATQ=APT+TAP (exterior angle is the sum of the opposite angles)
yet the angle ATP=180-(APT+TAP)
therefore ATP=180-ATQ
i.e. ATQ+ATP=180
Q,T,Pare collinear

anyone knows if this is legit ?
That assumes QTP is a straight line.
 

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