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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 $DPQ$...
by ahmedittihad
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 $M=(0,1/2,1/2)$ ...
by ahmedittihad
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.
by ahmedittihad
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?
by ahmedittihad
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.
by ahmedittihad
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. :(
by ahmedittihad
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...
by ahmedittihad
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. ...
by ahmedittihad
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.
by ahmedittihad
Tue Apr 11, 2017 10:30 pm
 
Forum: Combinatorics
Topic: Combi Marathon
Replies: 41
Views: 1275

Re: BDMO Forum Mafia #2

Zawadx wrote:
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.
by ahmedittihad
Tue Apr 11, 2017 4:55 pm
 
Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 27
Views: 726
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