Circle Geometry Question (1 Viewer)

pi-ka-chew · Jul 22, 2010

i'm having trouble doing this question:

Question is: Prove that angle PAB = <meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 12"><meta name="Originator" content="Microsoft Word 12"><link rel="File-List" href="file:///C:%5CUsers%5CMonica%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><link rel="themeData" href="file:///C:%5CUsers%5CMonica%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx"><link rel="colorSchemeMapping" href="file:///C:%5CUsers%5CMonica%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w

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Problem is, i don't think i can asssme RAP is a straight line because:
1. RA is dashed suggesting it's a different line to AP?
2. In the next part of the question, it says to "Prove that if S, B, Q and M are concyclic, then R, A and P are collinear".

i'm not sure how to do this proof without assuming RAP is a straight line.

random-1006 · Jul 22, 2010

pi-ka-chew said:
i'm having trouble doing this question:

Question is: Prove that angle PAB = <META name=ProgId content=Word.Document><META name=Generator content="Microsoft Word 12"><META name=Originator content="Microsoft Word 12"><LINK rel=File-List href="file:///C:%5CUsers%5CMonica%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><LINK rel=themeData href="file:///C:%5CUsers%5CMonica%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx"><LINK rel=colorSchemeMapping href="file:///C:%5CUsers%5CMonica%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml"><STYLE>  </STYLE>β

Problem is, i don't think i can asssme RAP is a straight line because:
1. RA is dashed suggesting it's a different line to AP?
2. In the next part of the question, it says to "Prove that if S, B, Q and M are concyclic, then R, A and P are collinear".

i'm not sure how to do this proof without assuming RAP is a straight line.

it is a straight line, just oppo angle cyclic quad add to 180, then angles on straight line add to 180

thats strange, questions should be other way round, ill look at it bit more now

pi-ka-chew · Jul 22, 2010

random-1006 said:
it is a straight line, just oppo angle cyclic quad add to 180, then angles on straight line add to 180

but can i really just assume it's a straight line? given the question following is to prove that it's a straight line.

ninetypercent · Jul 22, 2010

If S,B,Q,M are concyclic
then angle MQB = B (exterior angle of cyclic quadrilateral)
angle PAB = B (exterior angle of cyclic quadrilateral)

OR
you could assume RAP is a straight line

OR use some other method that I can't think of atm

random-1006 · Jul 22, 2010

pi-ka-chew said:
but can i really just assume it's a straight line? given the question following is to prove that it's a straight line.

strange, there are no tangent, we cant use angle in alternate segment

Questions a dud i reckon, wouldnt worry bout it, where did u get it from

pi-ka-chew · Jul 22, 2010

ninetypercent said:
If S,B,Q,M are concyclic
then angle MQB = B (exterior angle of cyclic quadrilateral)
angle PAB = B (exterior angle of cyclic quadrilateral)

OR
you could assume RAP is a straight line

OR use some other method that I can't think of atm

xD yeah, but unfortunately, the first two options are both assumptions that i'm not sure i can make. thanks for the suggestions though!

pi-ka-chew · Jul 22, 2010

random-1006 said:
strange, there are no tangent, we cant use angle in alternate segment

Questions a dud i reckon, wouldnt worry bout it, where did u get it from

haha yes i know! my teacher couldn't do it either.
it's from cambridge (which i think is a relatively good textbook) xD

ninetypercent · Jul 22, 2010

In the second part of the question, they told you that the points are concyclic. I'm not sure whether you can bring in the second part of the question into the first part

random-1006 · Jul 22, 2010

ninetypercent said:
In the second part of the question, they told you that the points are concyclic. I'm not sure whether you can bring in the second part of the question into the first part

uh no

thats why its the second part

pi-ka-chew · Jul 22, 2010

random-1006 said:
uh no

thats why its the second part

exactly my view.

so right now, i'm stuck!

random-1006 · Jul 22, 2010

If you connect BP, would that give two congruent triangles, im a bit rusty on this circle geometry, they like never do it any in uni, we used it to prove like one physics formula, and thats it

you are sure theres nothing else that it given

pi-ka-chew · Jul 22, 2010

random-1006 said:
If you connect BP, would that give two congruent triangles, im a bit rusty on this circle geometry, they like never do it any in uni, we used it to prove like one physics formula, and thats it

unfortunately no. all they have in common is the line BP. angles aren't/cannot be proved to be the same, other sides are (probably) not the same either.

don't worry about it.

your help and effort is muchly appreciated already.

ninety, thank you too!!

DVDVDVDV · Jul 23, 2010

Aren't there answers at the back of the book?

I use a different one, so I don't know.

Drongoski · Jul 23, 2010

pi-ka-chew: Pls post full wordings of question.

Very good you have a clear diagram. We need to be very clear as to what exactly are given and what need to be proven.

From my experience. proving 1) 3 or more points are collinear and 2) proving 3 or more lines are concurrent are among the hardest types of geometry problems.

pi-ka-chew · Jul 23, 2010

DVDVDVDV said:
Aren't there answers at the back of the book?

I use a different one, so I don't know.

unfortunately, the text book doesn't have worked solutions. xD

Drongoski said:
pi-ka-chew: Pls post full wordings of question.

Very good you have a clear diagram. We need to be very clear as to what exactly are given and what need to be proven.

From my experience. proving 1) 3 or more points are collinear and 2) proving 3 or more lines are concurrent are among the hardest types of geometry problems.

um... the diagram is as precise as i can make it.

questions:

i. Prove that angle PAB = β
ii. Prove that if S, B, Q and M are concyclic, then R, A and P are collinear.
iii. Prove that if R, A and P are collinear, then SBQM is cyclic.

i'm capable of doing the last two parts, but it's just the first one i'm having problems with.

Drongoski · Jul 23, 2010

I've found this to be Q7(b) page 368 of Cambridge 3U - Yr 12 (my old edition).

I think there are insufficient conditions for you to prove angle PAB = beta

If I draw any 2 intersecting circles (unfortunately I don't know how to draw the diagram - as you have done beautifully), without the specification of additional conditions, I have been able to draw similar figures where angle PAB =/= beta without imposing the requirement that P, A and R being collinear.

In other words I'm suggesting the question is flawed; additional conditions are required. You must avoid the trap of drawing RAP as a straight line (partially dashed regardless) because if it were, you have nothing much to prove.

Drongoski · Jul 24, 2010

I think the question was meant to be worded something like this:

By proving angle PAB = angle BSR (beta):

ii) prove that if S, B, Q and M are concyclic then R, A and P are collinear

iii) prove that if R, A and P are collinear, then SBQM is cyclic.

This means that: R, A and P are collinear if and only if (i.e. iff) S, B, Q and M are concyclic.

The question then makes sense (to me at least). Your teacher cannot be blamed for not being able to prove the 1st part since it makes no sense.

pi-ka-chew · Jul 24, 2010

Drongoski said:
I've found this to be Q7(b) page 368 of Cambridge 3U - Yr 12 (my old edition).

I think there are insufficient conditions for you to prove angle PAB = beta

If I draw any 2 intersecting circles (unfortunately I don't know how to draw the diagram - as you have done beautifully), without the specification of additional conditions, I have been able to draw similar figures where angle PAB =/= beta without imposing the requirement that P, A and R being collinear.

In other words I'm suggesting the question is flawed; additional conditions are required. You must avoid the trap of drawing RAP as a straight line (partially dashed regardless) because if it were, you have nothing much to prove.

Drongoski said:
I think the question was meant to be worded something like this:

By proving angle PAB = angle BSR (beta):

ii) prove that if S, B, Q and M are concyclic then R, A and P are collinear

iii) prove that if R, A and P are collinear, then SBQM is cyclic.

This means that: R, A and P are collinear if and only if (i.e. iff) S, B, Q and M are concyclic.

The question then makes sense (to me at least). Your teacher cannot be blamed for not being able to prove the 1st part since it makes no sense.

yes, we use the old cambridge textbook too.
ahh i see now. thanks soo much Drongoski!!

beautifully explained.

thanks for your compliment on my "drawing" too. xD just gotta love paint!

Circle Geometry Question (1 Viewer)

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