ergh. Circle Geometry is annoying. (1 Viewer)

[xxJTxx]

:mad1: according to my tutor, its more worthwhile to become familiar with the rules and practice as many hsc style q's as possible, rather then do a textbook approach where each exercise is based on a particular theorem or a few particular theorems? is this true? has it worked for anyone? i dunno. im using the couchman and jones textbook and some of the questions in the exercises (chap 21) can just be very uber annoying.
this has discouraged me when it comes to circ geo. A LOT too.

 

[watatank]

The textbook approach doesnt hurt, because it does help....but I think its more worthwhile to be able to understand the rules and apply it to as many HSC style questions as possible...because thats where the teachers will get their questions from for assessments and all that.

 

[conman]

Better to do as many past papers as u can.

 

[pLuvia]

Past papers question are more similar to your forthcoming exam papers as they have the same layout and similar type of questions, although this year the MX1 paper was a bit random

But for basics just stick with textbook questions

 

[ianc]

Yeah circle geometry isnt really that difficult because you only know a few simple rules, so you can just try fiddling with each one until it works.

Here are 2 rules which pop up regularly in more challenging questions:


1. The cyclic quadrilateral.

Know how to find one-
* exterior angle = interior opposite angle
* opposite angles are supplementary.

Also, if you have a cyclic quad, then the angles in the same segment rule applies too - see diagram (the marked angles are equal)

- This can also be used to prove that something is a cyclic quad



2. Also, that big long rule - The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. - often comes up in more difficult questions.



Good luck with it and don't lose faith! Once you've worked through a few questions you'll realise that it is not too difficult.

 

[xxJTxx]

Wow, thanks for the help guys.

Now that ive finished with the exercises (no i didnt go do it all after i posted..i've been working on them for the last two days and today) i think it will be good to go and do heaps of past paper questions..as many as i can get.

i think ive moulded my approach around knowing all the rules in my head (and their converses when they apply) and just rehearsing them based on what i see in the question, then trying to solve..."fiddling around" with them as ianc put it.

cept. i am yet to understand the "angles in the same segment" rule...i totally dont get that. that cyclic quad that you drew up (awesome work btw lol), how are the equal angles that are labelled in the same segment? ive gotten the swing of the angle between a tangent and a chord through the point of contact is equal to the angle in the alt. segment...although, sometimes i guess the alt. segment.

 

[bos1234]

:mad1: according to my tutor, its more worthwhile to become familiar with the rules and practice as many hsc style q's as possible, rather then do a textbook approach where each exercise is based on a particular theorem or a few particular theorems? is this true? has it worked for anyone? i dunno. im using the couchman and jones textbook and some of the questions in the exercises (chap 21) can just be very uber annoying.
this has discouraged me when it comes to circ geo. A LOT too.

You should try and do both

 

[redom]

the angles in the same segement theoreom kinda got to me at first. Our teacher said something about the "angles being subtended by the same arc/chord are equal", which made it easier to understand.

 

[ianc]

Also - just remembered something else - sometimes youll like label one angle "alpha" and the other "beta" or something, then use the rules and a little algebra (perhaps even simultaneous equations) to work out the question. My teacher said that you'll never need to have more than 2 of these variables. This probably applies more to extension 2 circle geometry where you have to do some major mucking around, but it's useful to bear in mind so that you don't get too bogged down into a question.

And for the angles in same segment rule, redom's "angles being subtended by the same arc/chord are equal" is also a neat way to understand it if you find that easier.