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

[J2good4u]

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]

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

 

[J2good4u]

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

 

[SpiralFlex]

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.
.

 

[panda15]

This line is not valid. Therefore the lines below are not valid.
.

+1. You assumed the result you were trying to prove, so not valid.

 

[AnimeX]

+1. You assumed the result you were trying to prove, so not valid.

is this a zero out of three? I did this aswell unfortunately, wasn't thinking straight

 

[drunkenmonkee37]

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]

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.

 

[RealiseNothing]

is this a zero out of three? I did this aswell unfortunately, wasn't thinking straight

But QTP sure was

 

[SpiralFlex]

But QTP sure was

..................

 

[aDimitri]

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]

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]

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.

 

[liuque]

That assumes QTP is a straight line.

I'm screwed