Search found 181 matches
- Wed Jan 11, 2017 4:55 pm
- Forum: National Math Olympiad (BdMO)
- Topic: National BDMO 2016 : Junior 8
- Replies: 4
- Views: 11047
Re: National BDMO 2016 : Junior 8
This was a nice problem. Let $C'$ be the reflection of $C$ w.r.t $BP$. Now, $\angle C'BC = 2*10$. So, $\angle QBC'=80-20=60$. As $QB=6, BC'=12$ and $\angle QBC' =60$ we see that $\triangle QBC'$ is a $30-60-90$ triangle. So, $\angle BQC'=90$. We get, $BQC'P$ is cyclic. So, $\angle CPQ= \angle BPC+\a...
- Sun Jan 08, 2017 3:21 pm
- Forum: Geometry
- Topic: Geometry Marathon : Season 3
- Replies: 146
- Views: 277760
Re: Geometry Marathon : Season 3
Problem 11:
Let $ABC$ be a triangle inscribed circle $(O)$, orthocenter $H$. $E,F$ lie on $(O)$ such that $EF\parallel BC$. $D$ is midpoint of $HE$. The line passing though $O$ and parallel to $AF$ cuts $AB$ at $G$. Prove that $DG\perp DC$.
Let $ABC$ be a triangle inscribed circle $(O)$, orthocenter $H$. $E,F$ lie on $(O)$ such that $EF\parallel BC$. $D$ is midpoint of $HE$. The line passing though $O$ and parallel to $AF$ cuts $AB$ at $G$. Prove that $DG\perp DC$.
- Sat Jan 07, 2017 5:40 pm
- Forum: Geometry
- Topic: Proving concurrency at symmedian point.
- Replies: 4
- Views: 3763
Re: Proving concurrency at symmedian point.
I'd like if you shared the analytic solution here.
- Fri Jan 06, 2017 2:21 am
- Forum: Secondary Level
- Topic: TJMO 1996/2
- Replies: 4
- Views: 4222
Re: TJMO 1996/2
Trinary is the number system with base 3. Familiarize yourself with different number bases except the decimal one.siwomcre wrote:What is trinary?Raiyan Jamil wrote:Trinary should help.
- Wed Jan 04, 2017 9:09 pm
- Forum: Geometry
- Topic: Proving concurrency at symmedian point.
- Replies: 4
- Views: 3763
Proving concurrency at symmedian point.
Let $A'$ be the midpoint of $BC$. $B'$ and $C$' are labelled similarly. Let $D$ be the feet of perpendicular of $A$ vertex on $BC$. $P$ be the midpoint of $AD$. label $Q,R$ similarly. Prove that, $ A'P, B'Q$ and $C'R $are concurrent and intersect at the symmedian point of $ ABC$.
- Wed Jan 04, 2017 4:37 pm
- Forum: Introductions
- Topic: Late introduction
- Replies: 1
- Views: 8856
Late introduction
Hello people. I'm Ahmed Ittihad. I love problem solving. I have been doing BdMO for the last 6 years and I'm in class 10 now. Let's make this forum great again.
- Wed Jan 04, 2017 4:32 pm
- Forum: Introductions
- Topic: O hai all!
- Replies: 3
- Views: 9975
Re: O hai all!
" Good and bad are perspectively different."
- Wed Jan 04, 2017 3:47 am
- Forum: Site Support
- Topic: How to prepare and study for BdMO in Secondary Group
- Replies: 3
- Views: 17193
Re: How to prepare and study for BdMO in Secondary Group
Okay, the best thing to do for regionals is to practise the problems of the previous years. But studying some books have helpe me in the past. You can read 'BdMO prostuti' or 'songkhyatotto o combinatorics' by Mutasim Mim.
- Wed Jan 04, 2017 3:42 am
- Forum: Social Lounge
- Topic: need this question answer
- Replies: 1
- Views: 2564
Re: need this question answer
Study some notes about number systems. In this case, base $12$.
- Wed Jan 04, 2017 3:36 am
- Forum: Divisional Math Olympiad
- Topic: secondary dhaka divisional 2015
- Replies: 1
- Views: 2959
Re: secondary dhaka divisional 2015
Interestingly, this problem needs spiral similarity. So, we have, $\triangle DAB$ similar to $ \triangle DPQ $. By spiral similarity, $\triangle DQB $ similar to $ \triangle DPA $. So, $\angle DAP=\angle DBQ$. This is only possible when the parallelogram is a rectangle. We also have, for similarity ...