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

J2good4u

Member
Joined
Apr 25, 2011
Messages
75
Gender
Male
HSC
N/A
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
Joined
Dec 18, 2010
Messages
6,960
Gender
Female
HSC
N/A
Didn't you just post this on the circle geom thread?
 

J2good4u

Member
Joined
Apr 25, 2011
Messages
75
Gender
Male
HSC
N/A
Yes, but I posted it on a thread to get a direct answer...Well?
 

SpiralFlex

Well-Known Member
Joined
Dec 18, 2010
Messages
6,960
Gender
Female
HSC
N/A
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:
Joined
Apr 29, 2012
Messages
39
Gender
Male
HSC
2013
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
Joined
Feb 22, 2012
Messages
675
Gender
Male
HSC
2013
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

i'm the cook
Joined
Aug 22, 2013
Messages
505
Location
Blue Mountains
Gender
Male
HSC
2014
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
Joined
Sep 11, 2013
Messages
46
Gender
Female
HSC
2013
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
Joined
Jul 10, 2011
Messages
4,591
Location
Sydney
Gender
Male
HSC
2013
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.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top