Hi Everyone,
I am new here and i was just wondering if anyone had advice or any notes on how to
summarise the circle geometry laws. As i am finding it very hard to memorise
them, i have tried looking in the notes section but saddly couldn't find anything.
Any help would be appreciated even attachments that i can print out. Thank you
in advance to anyone who can help.
From Joshua.
When I first learnt circle geometry I had to take a while to drill in all those theorems.
Over time however, I managed to memorise what the circle geometry theorems "looked like" and why the words "made sense". Take two examples:
- Angles in the same segment (AKA angles standing on the same arc) are equal. They're literally angles on the same arc because the arc is essentially subtending both of the angles. But even though the theorem says they look the same, I always looked at the interesting inverted shape pattern it has. I eventually just associated it with that theorem.
- Alternate segment theorem. Sometimes called the surfboard theorem because of how it looks, but honestly I literally just memorised a triangle and a tangent. That was it.
Then I moved onto the key features. I thought about which theorems involved the centre of the circle/diameters, or which theorem involved tangents. And of course which theorems involved nothing special (i.e. only chords and secants).
Over time I had the words basically just associated to what it "looked" like. Last piece of the puzzle was remembering where everything actually went. With stuff like alternate segment theorem and the weirder cases of angle at centre = 2x angle at circumference this takes a bit more effort.
Still though, sitting down and focusing on them is not gonna do anything - practice problems are not avoidable. But because I knew what it all "looked" like. when I looked at a complicated diagram I just chose to not focus on the diagram in its entirety. Instead, I just looked at what I wanted to prove (or find), and "saw" what the theorems looked like to navigate my way across.
And then there's also other little things to watch out for e.g. angle chasing