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BdMO Online Forum • Search

## Search found 123 matches

### Re: Geometry Marathon : Season 3

Problem 42 Let \$ABC\$ be a triangle with altitudes \$AD,BE,CF\$ with \$D,E,F\$ are on sides \$BC,CA,AB\$, resp. Let \$O\$ be the circumcenter of triangle \$ABC\$. \$P,Q\$ are respectively on \$DE,DF\$ such that \$FP\perp AC\$ and \$EQ\perp AB\$. a) Prove that the midpoint \$K\$ of \$AO\$ is circumcenter of triangle \$DPQ\$...
Mon May 01, 2017 1:37 pm

Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 88
Views: 2350

### Re: Geometry Marathon : Season 3

Solution to Problem 41 Claim: Let \$IM\$ intersect the perpendicular from \$A\$ to \$BC\$ at \$G\$. \$GD \parallel AI\$. Proof: As \$AG \parallel ID\$, it would suffice to prove that \$AG=ID\$. Hence yielding \$AGDI\$ a parallelogram. We prove \$AG=ID\$ by barycentric coordinates. Plugging in points \$M=(0,1/2,1/2)\$ ...
Mon May 01, 2017 12:58 pm

Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 88
Views: 2350

### Re: Beginner's Marathon

I think you should give the full solution to the problems or give hints if the thread is stuck for some days.
Thu Apr 20, 2017 10:03 pm

Forum: Junior Level
Topic: Beginner's Marathon
Replies: 48
Views: 1595

### Re: BDMO Forum Mafia #2

Okay, guys. Would you want to take a preliminary vote to get some information? Or do you want to discuss about what might be our best strategy?
Thu Apr 20, 2017 8:24 pm

Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 27
Views: 726

### Re: A Lemma?

I think you have the wrong idea of elegance. To see what not elegant is, Thanic Nur Samin vaiya is your best choice.
Mon Apr 17, 2017 8:03 pm

Forum: Geometry
Topic: A Lemma?
Replies: 8
Views: 235

### Re: Another Ah moment

No one tried this problem. Me very sad.
Wed Apr 12, 2017 8:22 pm

Forum: Combinatorics
Topic: Another Ah moment
Replies: 1
Views: 76

### Re: BdMO 2017 junior/4

So basically you do different cases on the primes dividing \$n^2\$ or \$n-1\$. And these cases yield different divisibility conditions. And CRT is the method to find the smallest number that suppression every congruence in a system. Look it up. The notation might be scary but it's quite natural and intu...
Wed Apr 12, 2017 7:14 pm

Forum: National Math Olympiad (BdMO)
Topic: BdMO 2017 junior/4
Replies: 7
Views: 212

### Another Ah moment

You are given a TV screen with \$n×(n+2)\$ pixels(the dimension is \$n \$ on a side and \$n+2\$ on another side). Initially, there are \$k \$ pixels turned on. In any \$2×2\$ screen, as soon as there are \$3\$ unit screens which are off, you can turn off the \$4\$th screen. Your goal is to turn the whole TV off. ...
Wed Apr 12, 2017 1:29 am

Forum: Combinatorics
Topic: Another Ah moment
Replies: 1
Views: 76

### Re: Combi Marathon

Solution? And another problem please.
Tue Apr 11, 2017 10:30 pm

Forum: Combinatorics
Topic: Combi Marathon
Replies: 41
Views: 1275

### Re: BDMO Forum Mafia #2

This time, EVERYONE will get a special power role (no vanillas). Hopefully this will result in some fun for everyone!

.

"Everyone's super is another way to say no one is."

BTW, I'm playing.
Tue Apr 11, 2017 4:55 pm

Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 27
Views: 726
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