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# The Ultimate Maths Competition Thread

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1. 11234

Try this one as well. I've just solved it and it's a beauty.

Let ABC be an acute-angled triangle and let D, E be the feet of the perpendiculars from A, B to BC, CA respectively. Let P be the point where the line AD meets the semicircle constructed outwardly on BC, and Q be the point where the line BE meets the semicircle constructed outwardly on AC. Prove that CP = CQ.
2. (Original post by Maths465Man)
I got a nice solution to this question earlier.

ABCD is a rectangle, P is the midpoint of AB, and Q is the point on PD such that CQ is perpendicular to PD. Prove that triangle BQC is isosceles.
ok I'll have a look
3. (Original post by Renzhi10122)
Most definitely not. Go on 'the' IMO website, not the indian version for it. Basically, you have to be a citizen in the country you want to represent, or have studied for 3 years there. The indian one was for indian students, hence why they say that.
I see. And people of all ages can participate?
4. (Original post by Maths465Man)
11234

Try this one as well. I've just solved it and it's a beauty.

Let ABC be an acute-angled triangle and let D, E be the feet of the perpendiculars from A, B to BC, CA respectively. Let P be the point where the line AD meets the semicircle constructed outwardly on BC, and Q be the point where the line BE meets the semicircle constructed outwardly on AC. Prove that CP = CQ.
Could you give me a hint
5. (Original post by Wolfram Alpha)
I see. And people of all ages can participate?
Those less than 19 and not entered tertiary education
6. Just wondering, what are the average thresholds for Gold, Silver and Bronze in BMO1 ( i know last year's ones but Im interested in an average) and what is the average mark required in Maclaurin for medal/book prize? Thank you
7. (Original post by ben167)
Just wondering, what are the average thresholds for Gold, Silver and Bronze in BMO1 ( i know last year's ones but Im interested in an average) and what is the average mark required in Maclaurin for medal/book prize? Thank you
For bmo1 it jumps up and down tbh and i cnt find anywhere where all the boundaries are given. For gold try get 50+ is the only aim.

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8. Ok thank you. Is it the same for Maclaurin?
(Original post by physicsmaths)
For bmo1 it jumps up and down tbh and i cnt find anywhere where all the boundaries are given. For gold try get 50+ is the only aim.

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9. (Original post by 11234)
Could you give me a hint
Have you drawn the diagram correctly?
10. Ok, I've realised we shouldn't discuss the BMO1 or BMO2 questions here on this thread as the UKMT don't want solutions to be published. From now on, we shouldn't discuss BMO solutions to problems.
11. (Original post by Maths465Man)
Ok, I've realised we shouldn't discuss the BMO1 or BMO2 questions here on this thread as the UKMT don't want solutions to be published. From now on, we shouldn't discuss BMO solutions to problems.
I am sure you can discuss questions just don't write up a solutions bank.
12. (Original post by physicsmaths)
I am sure you can discuss questions just don't write up a solutions bank.
So is it ok if I post a solution to this thread?
13. (Original post by Maths465Man)
So is it ok if I post a solution to this thread?
i guess so well i ain't sure you can probably email geoff smith or something and ask him if discussing the problems and sharing each others solutions is ok. the latter is the only thing that might bother them although I did it all this year with BMO1 and BMO2 threads.
14. Approximately how many points do you need in Maclaurin to get into the summer school?
15. What sections of the AoPS website are useful for preparing for BMO1, BMO2, IMO etc?
16. What did you get on IMOK this year?
(Original post by Maths465Man)
What sections of the AoPS website are useful for preparing for BMO1, BMO2, IMO etc?
17. (Original post by ben167)
What did you get on IMOK this year?
60 on the Hamilton
18. I found this great PDF on preparing for Olympiads

19. Wow thats insane! I screwed up and got 33 on it
(Original post by Maths465Man)
60 on the Hamilton
20. Right lets keep this thread lively.

If m and n are relatively prime odd integers find the greatest common divisor of 5^m+7^m and 5^n and 7^n

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