HSC Stuff > HSC Mathematics Extension 2
Harder 3u- Circle Geo
hanaacdr:
Could i please get some help on this question?
RuiAce:
--- Quote from: hanaacdr on January 27, 2017, 09:26:17 pm ---Could i please get some help on this question? (Image removed from quote.)
--- End 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:
--- Quote from: hanaacdr on January 27, 2017, 09:26:17 pm ---Could i please get some help on this question? (Image removed from quote.)
--- End 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:
--- Quote from: RuiAce on January 27, 2017, 09:50:44 pm ---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.
--- End quote ---
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"??
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