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Thread: How do i get better at Circle Geometry?

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    Post How do i get better at Circle Geometry?

    Okay so, I'm in year 10 at the moment and its the 6 week holiday into year 11. I have been going through numerous textbook's and I can do most topics except circle geometry. I can somewhat do the questions but I cant finish them without looking at the answer. It's always those "Prove" questions that get me. I just don't know how to structure them. Do you guys have any tips on mastering circle geometry?

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    Re: How do i get better at Circle Geometry?

    Yeah I hated circle geometry too when I was in Year 11 and Year 12. Here's a few pointers that helped me but I don't know if it'll help much for you since they're pretty basic:

    - Always go 'angle hunting' whenever you see a big 3 or 4 mark circle geometry question. Normally, the tougher questions require really obscure information and sometimes you won't be able to recognise them without knowing the values of certain angles. Also, knowing as many angles as possible can help you identify the presence of perhaps alternate angles (when proving that two lines are parallel) or maybe when proving that there is a cyclic quadrilateral. My advice is to go angle hunting for all circle geometry questions to begin with if you have the time (even if the questions are only like 1 or 2 marks).

    - This tip is really basic but I legit just learned this like at the end of Year 11 which was pretty sad. So you know how cyclic quadrilaterals are when opposite angles of a quadrilateral (whose corners are touching the circumference of the circle) are supplementary (I think)? I didn't realise that the 'angles in the same segment' theorem can also be used to show a cyclic quadrilateral. This can be pretty handy in exams.

    - Whenever you see a 'butterfly' looking shape in a circle like this http://www.timdevereux.co.uk/maths/g...s/proof3_a.gif , then the question will almost always require angle in the same segment theorem. This is really useful especially when the diagram becomes a bit more convoluted like this http://community.boredofstudies.org/...circlegeom.png
    (note how we can use this theorem for triangle DAB and triangle DPC)

    - Whenever you see a tangent, then there's probably gonna be the 'angle in alternate segment' theorem.

    Anyways I don't know if these tips helped - you might already know all of this but it helped me personally for my HSC.

    In terms of structuring response, just list out all of your steps as usual (like proving similar triangles). Just write your reason in brackets (like angle in same segment or whatever) and always state what side or angle you're referring to.

    I would recommend copying to diagram in your writing exam booklet if you have the time. Also, if you need to draw another line in the diagram, just say 'construct line DC' or something like that.

    Finally, the best way to master circle geometry is through practice. There's really no shortcut except doing many questions. And also, I would recommend looking at the circle geometry questions during reading time of an exam - you can normally figure out how to prove something in your head for the simpler circle geometry questions.

    Good luck!
    Last edited by captainhelium; 10 Jan 2018 at 9:37 PM.
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    Re: How do i get better at Circle Geometry?

    Going on with captainhelium's angle hunting method, if you have no idea how to start a question I recommend identifying angles that are equal (using theorems) and use pronumerals to label them. This could get pretty messy once you start bringing in other pronumerals but I find that this helps quite a lot because sometimes I end up solving the question even though I wasn't aiming to do so just yet.

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    Re: How do i get better at Circle Geometry?

    Really just comes down to practice. Do lots and lots of questions. It could also help to "work backwards" from what they ask you to prove.

    Most of the time if I don't know where to start, I start marking angles with small dots or other symbols before deciding whether to assign them pronumerals, this might help to prevent labelling becoming messy?
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    Re: How do i get better at Circle Geometry?

    An indirect approach is to try and prove the circle geometry theorems that you are using. Start with some basic ones like why the angles at the circumference are half the angle at the centre etc.

    Draw a big accurate diagram.

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    Re: How do i get better at Circle Geometry?

    My teacher made me memorise the proof and tested me back to front

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    Re: How do i get better at Circle Geometry?

    Literally spam questions no joke

    After a while you'll start to recognise methods quickly it's pretty simple just do heaps of questions

    ALSO DRAW A HUGE GIGANTIC DIAGRAM so you can easily see info
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    Re: How do i get better at Circle Geometry?

    Quote Originally Posted by HeroWise View Post
    My teacher made me memorise the proof and tested me back to front

    Don't know what exactly you mean by "memorise". If it is what I think it is, then I think it is a dumb way to learn circle geometry. How many solutions are you going to memorise?
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    Re: How do i get better at Circle Geometry?

    Quote Originally Posted by Drongoski View Post
    Don't know what exactly you mean by "memorise". If it is what I think it is, then I think it is a dumb way to learn circle geometry. How many solutions are you going to memorise?
    I think he meant memorise the theorems

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    Re: How do i get better at Circle Geometry?

    answering op:
    1. memorise theorems.
    2. draw diagram of question.
    3. angle hunt.
    4. after you've reached the angle you want, look through your angle hunt and find the most efficient "route" to get to your final answer. what steps did you take to reach the end?
    5. write down those steps, then beside each step, in brackets, write the theorem you used
    6. practise, practise, practise

    i guess it would help a lot to have someone walk you through these steps for like 5-10 questions, so you get how it works. scaffolded instruction is probably the most effective way to learn maths. teacher does the work, do the work together, then do it by yourself.

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