The Ultimate Maths Competition Thread

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.

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.

@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.

I see. And people of all ages can participate?

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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Could you give me a hint

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.

So is it ok if I post a solution to this thread?

What sections of the AoPS website are useful for preparing for BMO1, BMO2, IMO etc?

What did you get on IMOK this year?

60 on the Hamilton