Search found 176 matches
- Sun Mar 03, 2013 10:29 pm
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 8016
Re: A Very Nice Problem
Oops, missed that one!
- Sun Mar 03, 2013 12:24 am
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 8016
Re: A Very Nice Problem
My avatar is the sign of an anime character. He's awesome!
- Fri Mar 01, 2013 5:43 pm
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 8016
Re: A Very Nice Problem
The solution with butterfly seems long but uses many beautiful ideas. Let $H$ be the orthocentre and $AH \cap BC=D$. By homothety, we can show that, $A_2, M, H$ are collinear. Let $AH \cap O=P$. By angle chasing we can show that, $P, D, S$ are collinear. Now, using butterfly on chords $A_2P$ and $SA...
- Mon Feb 25, 2013 6:57 pm
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 8016
Re: A Very Nice Problem
Yeah, yeah, this is a problem that Zadid made himself thinking of using Butterfly. But as now it's exposed, anyone can give the proof using butterfly. If anyone doesn't, then I'd give Zadid's solution. Or Zadid could give it himself.
- Sun Feb 24, 2013 9:58 pm
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 8016
Re: A Very Nice Problem
Hmm, Sourav gave the same one. This is the solution most people would give. I was hoping for another way. Can anyone try it in a different way?
- Sun Feb 24, 2013 11:10 am
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 8016
A Very Nice Problem
Let $O$ be the circumcircle of triangle $ABC$. Let $AS$ and $AM$ be the symmedian and median respectively. Let $AS \cap O=S$ and $AM \cap BC=M$. Let $SM \cap O=A_1$ and let $A_2$ be the diametrically opposite point of $A$. Let $A_1A_2 \cap BC=A_3$. Similarly define $B_3$ and $C_3$. Prove that, $AA_3...
- Fri Feb 15, 2013 11:29 am
- Forum: Secondary Level
- Topic: Geometry Note
- Replies: 6
- Views: 4966
Re: Geometry Note
It's good really.
- Fri Feb 15, 2013 11:26 am
- Forum: Social Lounge
- Topic: Happy VALENTINE
- Replies: 4
- Views: 5721
Re: Happy VALENTINE
Khali tui? :@
- Mon Feb 11, 2013 4:06 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Higher Secondary 8
- Replies: 6
- Views: 6195
Re: BdMO 2013 Higher Secondary Problem 8
Hint:
How and why did I miss this? :'(
- Mon Feb 11, 2013 4:01 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO 2013 Higher Secondary Problem 9
- Replies: 3
- Views: 4257
Re: BdMO 2013 Higher Secondary Problem 9
Let $AD \cap EF=T$, $BE \cap CD=S$, $AB \cap CF=K$, $AE \cap BD=L$, $CR \cap FQ=M$. Then use Pascal's theorem and Desaurge's theorem to prove that $P, Q, T; P, R, S; R, Q, K; X, O, M; L, M, P; X, L, P$ are collinear (I'm leaving this tedious job to you guys, I can't write it). And it implies that $X...