Harder 3u- Circle Geo

[hanaacdr]

Could i please get some help on this question?

[RuiAce]

Could i please get some help on this question? (Image removed from quote.)

You're not going to get anywhere unless you start annotating/drawing on that diagram. Or copy it out if you want.

Hint to get you started off: ∆AKM ||| ∆ABC. This becomes clearer as soon as you join the lines KM and ML, which is absolutely necessary for (i)

[de]

Could i please get some help on this question? (Image removed from quote.)

i)
Since K and M are midpoints so KM is parallel to BC and thus to BL.(think about this just as a dilation (stretch) centred at A then it is very intuitive)
Since L is the midpoint of BC and M is the midpoint of AC, ML is parallel to AB and thus to KB and we have, combining these two,that KLMB is a parallelogram.

ii)
Angle KPB is supplementary to KPL since it lies on a line which is supplementary to angle KML since they are opposite angles in a cyclic quad. so KPB=KML
iii)
From ii KPB=KML=KBP from i
So KBP is isosceles with KB=KP and since K is a midpoint KB=KP=KA now think about a circle centred at K with radius KP clearly AB is a diameter so  BPA is a right angle and we are done.

[RuiAce]

Not too sure if the 'dilation' shortcut is taught...

I know that intercepts on transversals on parallel lines are taught, but not sure about the triangle dilation. Probably is taught, but with another name.
________________

Anyway, that's the question done above. Reminder that the emphasis is on you drawing out a diagram. This is why I purposely chose not to provide the full solution YET at the time of posting.

[de]

Not too sure if the 'dilation' shortcut is taught...

I know that intercepts on transversals on parallel lines are taught, but not sure about the triangle dilation. Probably is taught, but with another name.
________________

Anyway, that's the question done above. Reminder that the emphasis is on you drawing out a diagram. This is why I purposely chose not to provide the full solution YET at the time of posting.

Yeah, dilation probably isn't taught as such, but that was just an intuitive way of seeing what I think is called the "midpoint theorem"??

[RuiAce]

Yeah, dilation probably isn't taught as such, but that was just an intuitive way of seeing what I think is called the "midpoint theorem"??

It could be called that I suppose.

Found it on the syllabus for other's reference. Weird, because I must've overlooked it in the past. Refer to page 23.

It's definitely the easiest way of tackling (i).

[aryak]

How can you solve circle geometry questions under time limits and pressure? I am finding it really hard to do.

[jamonwindeyer]

How can you solve circle geometry questions under time limits and pressure? I am finding it really hard to do.

Hey! Unfortunately, there is no hidden secrets - It is just practice. The more questions you do, the better you will become!

I'd also suggest that you leave Circle Geo questions until last in your exam - It takes the pressure off if you know that you've done everything else you possibly can. You don't have questions waiting. That way you can just focus on the question without stressing about anything you have to do later in the paper