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

#### J2good4u

##### Member
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

##### Well-Known Member
Didn't you just post this on the circle geom thread?

#### J2good4u

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

#### SpiralFlex

##### Well-Known Member
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. .

Last edited:

#### panda15

##### Alligator Navigator
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

##### Member
+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

##### Member
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

##### Alligator Navigator
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

##### what is that?It is Cowpea
is this a zero out of three? I did this aswell unfortunately, wasn't thinking straight
But QTP sure was

#### SpiralFlex

##### i'm the cook
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

##### Member
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

##### what is that?It is Cowpea
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

##### Member
That assumes QTP is a straight line.
I'm screwed 