Search found 55 matches

by nahin munkar
Mon Feb 27, 2017 1:27 am
Forum: Social Lounge
Topic: ক্যাম্প
Replies: 4
Views: 427

Re: ক্যাম্প

ahmedittihad wrote:আমি ক্যাম্পে ডাক পেতে চাই। আমি এবার জাতীয় তে তৃতীয় হয়েছি। প্রথম দুইজন যদি উধাও হয়ে যায় তাহলে কি আমার ক্যাম্পে চান্স পাবার সম্ভাবনা বৃদ্ধি পাবে?
আমার মনে হয় সম্ভাবনা বৃদ্ধি না পেয়ে উল্টা কইমা যাবে । কারণ, প্রথম দুইজন রসগোল্লার মত উধাও হইলে তৃতীয় জনেরও উধাও হওয়ার বিপুল সম্ভাবনা আছে।
by nahin munkar
Sun Feb 26, 2017 11:52 pm
Forum: Social Lounge
Topic: Favorite mathematician?
Replies: 30
Views: 3708

Re: Favorite mathematician?

Carl Friedrich Gauss :)
by nahin munkar
Wed Feb 15, 2017 12:27 am
Forum: National Math Olympiad (BdMO)
Topic: BDMO 2017 National round Secondary 5
Replies: 2
Views: 403

Re: BDMO 2017 National round Secondary 5

A synthetic solution : We denote the inscribed circle as $\omega$ , & $P,Q$ be the tangent point of arc $BC$ & $AB$ resp with $\omega$. We get, $AB=AC=r$ (radii of same circle) & $AB=BC$ similarly. $\Longrightarrow AB=AC=BC \Longrightarrow \triangle ABC$ is equilateral $\Longrightarrow \angle B =60...
by nahin munkar
Tue Jan 10, 2017 1:32 am
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

Re: Geometry Marathon : Season 3

Problem 14 Let one of the intersection points of two circles with centres $O_1,O_2$ be $P$. A common tangent touches the circles at $A,B$ respectively. Let the perpendicular from $A$ to the line $BP$ meet $O_1O_2$ at $C$. Prove that $AP\perp PC$. Solution of problem 14 : Let , the radical axis of t...
by nahin munkar
Mon Jan 09, 2017 2:59 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

Re: Geometry Marathon : Season 3

Now, an easy.problem :D Problem 12: Let $\triangle ABC$ be scalene, with $BC$ as the largest side. Let $D$ be the foot of the perpendicular from $A$ on side $BC$. Let points $K,L$ be chosen on the lines $AB$ and $AC$ respectively, such that $D$ is the midpoint of segment $KL$. Prove that the points ...
by nahin munkar
Mon Jan 09, 2017 12:15 am
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

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 $DG\perp DC$. Solution of problem 11 : We first denote some extra point...
by nahin munkar
Fri Jan 06, 2017 8:59 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

Re: Geometry Marathon : Season 3

Problem 4: Let $ABC$ be a triangle and $m$ a line which intersects the sides $AB$ and $AC$ at interior points $D$ and $F$, respectively, and intersects the line $BC$ at a point $E$ such that $C$ lies between $B$ and $E$. The parallel lines from the points $A$, $B$, $C$ to the line $m$ intersect the...
by nahin munkar
Fri Jan 06, 2017 8:19 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

Re: Geometry Marathon : Season 3

$\text{Problem 3:}$ In Acute angled triangle $ABC$, let $D$ be the point where $A$ angle bisector meets $BC$. The perpendicular from $B$ to $AD$ meets the circumcircle of $ABD$ at $E$. If $O$ is the circumcentre of triangle $ABC$ then prove that $A,E$ and $O$ are collinear. Solution of problem 3 : ...
by nahin munkar
Fri Jan 06, 2017 7:16 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

Re: Geometry Marathon : Season 3

Problem 2 In $\triangle ABC$, $\angle ABC=90^{\circ}$. Let $D$ be any point on side $AC$, $D \neq A,C$. The circumcircle of $\triangle BDC$ and the circle with center $C$ and radius $CD$ intersect at $D,E$. Let $F$ be a point on side $BC$ so that $AF \parallel DE$. $X$ is another point on $BC$(Diff...
by nahin munkar
Thu Jan 05, 2017 11:42 pm
Forum: Geometry
Topic: Geometry Marathon : Season 3
Replies: 110
Views: 5185

Geometry Marathon : Season 3

$\Re$evived $\Re$ules : Let's revive geo marathon (after 6 yrs only :mrgreen: ) . The rules will be almost same as before, just enhance solving time duration for 2 days . The difficulty level should be around G1-G5 compared with ISL(IMO Shortlist). Solver will post his own solution of the former pr...