## Search found 86 matches

Wed Feb 01, 2017 2:24 am
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 48411

### Re: Geometry Marathon : Season 3

Problem 18: Let $ABC$ be a triangle with circumcircle $\omega$ and let $H, M$ be orthocenter and midpoint of $AB$ respectively. Let $P,Q$ be points on the arc $AB$ of $\omega$ not containing $C$ such that $\angle ACP=\angle BCQ < \angle ACQ$.Let $R,S$ be the foot of altitudes from $H$ to $CQ,CP$ re...
Wed Feb 01, 2017 1:02 am
Topic: BdMO National Secondary: Problem Collection(2016)
Replies: 17
Views: 4225

### Re: BdMO National Secondary: Problem Collection(2016)

Wed Feb 01, 2017 12:55 am
Topic: BDMO national 2016, junior 10
Replies: 7
Views: 2238

### Re: BDMO national 2016, junior 10

I knew this problem was pretty much bland and disgusting. So, I just copied the solution from AOPS. Just copying took me 15 minutes. Allah knows how much time it took for the person to write. :P Haha! :lol: It may be a well known NT problem. So sad that in bdmo national 2016 Junior Category's some ...
Wed Feb 01, 2017 12:45 am
Topic: BdMO National Secondary: Problem Collection(2016)
Replies: 17
Views: 4225

Problem 6(b): (b) $DO \cap BI$ $= E$. In $\triangle EIO,$ $\angle IOE + \angle EOI + \angle EIO = 180^{\circ}$. and also, $\angle EIO = \angle ICB+\angle CBI$ $\angle IEO = 180^{\circ} - ( \angle EOI + \angle EIO)$ $\dots (1)$ $AC = BC$ and $BIOD$ is a cyclic quadrilateral. $\angle EOI + \angle EI... Wed Feb 01, 2017 12:12 am Forum: National Math Olympiad (BdMO) Topic: BdMO National Secondary: Problem Collection(2016) Replies: 17 Views: 4225 ### Re: BdMO National Secondary: Problem Collection(2016) Problem 6(a): (a) NO, the lines$AC$and$DI$doesn't intersect because they are parallel. Claim 1:$I, O, C$are collinear. Proof:$AC = BC$, So,$\angle BAC = \angle ABC$. O is the circumcenter of$\triangle$,$\angle OAB = \angle OBA$. So,$\angle OAC = \angle OBC$. Again,$\triangle OAC \con...
Tue Jan 31, 2017 11:42 pm
Topic: BdMO National Secondary: Problem Collection(2016)
Replies: 17
Views: 4225

### Re: BdMO National Secondary: Problem Collection(2016)

Tue Jan 31, 2017 11:38 pm
Topic: BdMO National Secondary: Problem Collection(2016)
Replies: 17
Views: 4225

### Re: BdMO National Secondary: Problem Collection(2016)

Problem 2 (a): (a) Factoring, $600 = 2^4 \times 3 \times 5^3$ $\therefore$ $600$ has $(4+1) (1+1) (3+1) = 40$ positive integers factor. Problem 2 (b): (b) Positive integer factors of $6000$ are perfect squares are $6$ in numbers. $\therefore$ $600$ has $(40 - 6) = 34$ positive integer factors which...
Tue Jan 31, 2017 11:23 pm