## Search found 36 matches

Wed Jan 09, 2019 1:39 pm
Forum: Social Lounge
Topic: BDMO Forum Mafia #2
Replies: 30
Views: 3967

### Re: BDMO Forum Mafia #2

HughDan wrote:
Thu Nov 22, 2018 5:28 pm
This seemed to be so much fun. Why not try to revive it? Sun Sep 02, 2018 1:13 pm
Forum: Social Lounge
Replies: 53
Views: 6318

♪＼(*＾▽＾*)／＼(*＾▽＾*)／
Tue May 15, 2018 8:25 pm
Forum: Social Lounge
Replies: 53
Views: 6318

┌∩┐(◣_◢)┌∩┐
Thu Apr 19, 2018 10:25 pm
Forum: Geometry
Topic: EGMO 2018 P5
Replies: 2
Views: 511

Let $N$ be the intersection point of $(ABC)$ and the angle bisector of $\angle{ACB}$ other than $C$ Suppose $\Omega$ touches $\tau$ at $L$ and $AB$ at $M$ Let $M'=NL \cap AB$ and $XY$ be the common tangent of $\tau$ and $\Omega$ Define $K=XY \cap AB$ $KM=KL$ $\measuredangle KLM' = \measuredangle KLN... Thu Apr 19, 2018 10:21 pm Forum: Geometry Topic: EGMO 2018 P5 Replies: 2 Views: 511 ### EGMO 2018 P5 Let$\tau$be the circumcircle of triangle$ABC$. A circle$\Omega$is tangent to the line segment$AB$and is tangent to$\tau$at a point lying on the same side of the line$AB$as$C$. The angle bisector of$\angle{BCA}$intersects$\Omega$at two different points$P$and$Q$. Prove that,$\angle...
Wed Apr 18, 2018 6:31 pm
Forum: Secondary Level
Topic: Easy Projective Geo
Replies: 3
Views: 726

We get $ACDE$ as an isosceles trapezoid Angle chasing gives us that $\angle{ABE}=\angle{DBC}$ Let $Q$ be the intersection point of $AC$ and $BD$. Again, $(A,C;Q,P)$ is a harmonic bundle $\frac{AQ}{CQ}=\frac{AP}{CP}$ Now it is enough to show that $BD$ is a symmedian Which means to show, $\frac{AB^2}{... Sun Apr 15, 2018 10:05 pm Forum: National Math Camp Topic: 2018 NT exam P2 Replies: 0 Views: 378 ### 2018 NT exam P2 Let$a_1, a_2, ....., a_n$be a sequence of real numbers such that$a_1+a_2+......a_n=0$and define$b_i=a_1+a_2+......a_i$for $$1\leq i \leq n$$. Suppose that $$b_i(a_{j+1}-a_{i+1})\geq 0$$ for all $$1\leq i \leq j \leq n-1$$. Show that max |$a_l$|$\geq$max |$b_m$|$(1 \leq l \leq n)$and$(1 \l...
Thu Apr 12, 2018 3:43 pm
Forum: Number Theory
Topic: 2018 BDMO NT exam P4
Replies: 2
Views: 564

### 2018 BDMO NT exam P4

Let $n$ be an even positive integer. A sequence of $n$ real numbers is called complete if for every integer $m$ with $$1 \leq m \leq n$$ either the sum of the first $m$ terms or the sum of the last $m$ terms is integral. Determine the minimum number of the integers in a complete sequence of $n$ numb...
Mon Apr 09, 2018 5:21 pm
Forum: Geometry
Topic: BAYMAX is cyclic!
Replies: 1
Views: 321