Search found 60 matches

by Dustan
Mon Apr 12, 2021 11:36 am
Forum: Social Lounge
Topic: Is it very late to start my math journey and participate in IMO?
Replies: 2
Views: 47

Re: Is it very late to start my math journey and participate in IMO?

NO!!!
But learning math is >>>>>>>>>> participating in national olympiad.
by Dustan
Fri Apr 02, 2021 5:41 pm
Forum: Secondary Level
Topic: Midcircles!!!
Replies: 2
Views: 72

Re: Midcircles!!!

This is known as incenter excenter lemma
by Dustan
Tue Mar 30, 2021 10:37 am
Forum: Algebra
Topic: FE Marathon!
Replies: 96
Views: 4613

Re: FE Marathon!

PROBLEM 23:
Find all continuouos functions $ f: \mathbb{R}\to\mathbb{R} $ such that for all reals $ x $ and $ y $
$ f(x+f(y))=y+f(x+1) $ .
by Dustan
Tue Mar 30, 2021 10:10 am
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 61460

Re: Geometry Marathon : Season 3

Asif Hossain wrote:
Tue Mar 30, 2021 8:58 am
Mehrab4226 wrote:
Mon Mar 29, 2021 10:08 pm
Asif Hossain wrote:
Mon Mar 29, 2021 10:01 pm

What did you meant by inside of $\angle BMA$??(sry if this sound foolish)
I think he meant $\triangle BMA$
then i think the $TX=BX$ holds iff $T=B$
i don't think so🤔
by Dustan
Sun Mar 28, 2021 9:14 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 61460

Re: Geometry Marathon : Season 3

Let $ABC$ be a triangle with incentre $I$. The circle through $B$ tangent to $AI$ at $I$ meets side $AB$ again at $P$. The circle through $C$ tangent to $AI$ at $I$ meets side $AC$ again at $Q$. Prove that $PQ$ is tangent to the incircle of $ABC.$
by Dustan
Sun Mar 28, 2021 9:09 pm
Forum: Social Lounge
Topic: PROLAP BOKA SECTION
Replies: 10
Views: 264

Re: PROLAP BOKA SECTION

বলে নি এখনো
by Dustan
Sun Mar 28, 2021 3:42 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 146
Views: 61460

Re: Geometry Marathon : Season 3

$ACPM$ and $BCQN$ are cyclic.
$\angle PCM=\angle PAM=\frac{A}{2}$
$\angle ACN=\angle QBA=\frac{B}{2}$
So,$\angle MCN=90-\angle ACN-\angle BCM=90-\frac{1}{2}(A+B)=90-45=45$
by Dustan
Sun Mar 28, 2021 2:42 pm
Forum: Social Lounge
Topic: PROLAP BOKA SECTION
Replies: 10
Views: 264

Re: PROLAP BOKA SECTION

২টা হবে মেবি।ঠিকবো না এবার!
by Dustan
Sat Mar 27, 2021 9:27 pm
Forum: Divisional Math Olympiad
Topic: BdMO Regional 2021 Higher Secondary P8
Replies: 16
Views: 899

Re: BdMO Regional 2021 Higher Secondary P8

I didn't think about $f$ could be bijective. :cry: :cry: :cry: So it gave me a weird solution, a huge one in fact. you are much better than me i $f(f(x))=x$ reminded me of involution and i knew that the function is bijective but i thought the question wanted $f(x)$ in $x$ terms so i gave the ans $0...
by Dustan
Sat Mar 27, 2021 5:08 pm
Forum: Divisional Math Olympiad
Topic: BdMO Regional 2021 Higher Secondary P8
Replies: 16
Views: 899

Re: BdMO Regional 2021 Higher Secondary P8

Mehrab4226 wrote:
Sat Mar 27, 2021 4:43 pm
I didn't think about $f$ could be bijective. :cry: :cry: :cry:
So it gave me a weird solution, a huge one in fact.
what is your ans then?