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OMK 2018 Olimpiad Matematik Kebangsaan Malaysian Sulong Question and Solutions Malaysian National Mathematical Olympiad

ByAnonymous Christian

Please find my attempt at Solutions for the OMK 2018 Olimpiad Matematik Kebangsaan Malaysian Highest-Sulong Category (Form 5, Lower & Upper Sixth Form, ages 17 to 19 inclusive) for the Malaysian National Mathematical Olympiad 2018.

Question and Solutions are in Images below.

Please try the questions by yourself first before looking at the suggested solutions presented here.

 

Thanks to PERSAMA for the freely downloadable Questions at the link below (source):

https://www.persama.org.my/omk/contoh-soalan-omk

Let’s Begin.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Edifying Comment:
 
Notice that we have Proven above that point P’ lies on both circles 1 and 2.
 
What is a consequence of this?
 
If P is not equal to P’,
 
Then circles 1 and 2 would have three intersection points, A, P and P’ which is a contradiction as two circles may intersect at at most 2 points.
 
Hence it must be that P = P’.

 

(which is a better argument than the one in Image next)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I hope that my personal solutions above are correct and yes, you may reproduce it and use it in any way you like (both commercially or non-commercially) for your benefit. Thank You God for everything.

Peace to you.

 

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