Search found 176 matches

by Thanic Nur Samin
Sat Jan 25, 2014 9:12 pm
Forum: Secondary Level
Topic: Greece NMO 2013#P4
Replies: 2
Views: 2432

Re: Greece NMO 2013#P4

$\Delta ABC$ is inscribed in $c$ =>$c$ is the circumcircle of $\Delta ABC$ =>$c$ crosses the points $A,B,C$. Again,the circumcircles $c_1,c_2,c_3$ intersect $\Delta BOD$,$\Delta COD$,$\Delta AEZ$ in B,C and A [Circumcircles intersect the points of the triangle] But c crosses the points too.So they ...
by Thanic Nur Samin
Tue Jan 21, 2014 11:20 pm
Forum: Algebra
Topic: Trouble in Trigonometry
Replies: 3
Views: 1559

Re: Trouble in Trigonometry

$sin5x$ $= sin5x + sinx - sinx$ $= 2 sin3x cos2x - sinx$ $= 2 (3sinx - 4sin^3 x) (1 - 2sin^2 x) - sinx$ $= 2 (8sin^5 x - 10sin^3 x + 3sinx) - sinx$ $= 16sin^5 x - 20sin^3 x + 5sinx$ Putting x=6, we get: $sin30= 16sin^5 6 - 20sin^3 6 + 5sin6$ Solving the equation, we get, $sin6=.105...$,so $cos6=\sqr...
by Thanic Nur Samin
Sun Jan 19, 2014 11:42 am
Forum: Divisional Math Olympiad
Topic: Chittagong Junior 2013 / 9
Replies: 1
Views: 1171

Re: Chittagong Junior 2013 / 9

O,F যোগ করি। OF=ব্যাসার্ধ=OA=10। এখন, $OE^2+OG^2=OF^2=10^2=100.......(1)$ $2(OE+OG)=24$বা$OE+OG=12$বা$OE=12-OG..............(2)$ (1)নং এ বসিয়ে পাই, $(12-OG)^2+OG^2=100=> 2OG^2-24OG+144=100=> OG^2-12OG+22=0=> OG=6-\sqrt{14}$ অর্থাৎ, $OE=6+\sqrt{14}$ $OG=12-OE=6-\sqrt{14}$ কিন্তু বৃত্তকলা $(AOB)=\fr...
by Thanic Nur Samin
Sat Jan 18, 2014 10:00 pm
Forum: Secondary Level
Topic: A Problem !!
Replies: 5
Views: 2138

Re: A Problem !!

3
2,2,11
3,5,7
5,5,5
by Thanic Nur Samin
Fri Jan 17, 2014 9:15 pm
Forum: Junior Level
Topic: REGIONAL OLYMPIAD PROBLEM
Replies: 4
Views: 2155

Re: REGIONAL OLYMPIAD PROBLEM

O,F যোগ করি। OF=ব্যাসার্ধ=OA=10। এখন, $OE^2+OG^2=OF^2=10^2=100.......(1)$ $2(OE+OG)=24$বা$OE+OG=12$বা$OE=12-OG..............(2)$ (1)নং এ বসিয়ে পাই, $(12-OG)^2+OG^2=100=> 2OG^2-24OG+144=100=> OG^2-12OG+22=0=> OG=6-\sqrt{14}$ অর্থাৎ, $OE=6+\sqrt{14}$ $OG=12-OE=6-\sqrt{14}$ কিন্তু বৃত্তকলা $(AOB)=\fra...
by Thanic Nur Samin
Mon Dec 09, 2013 11:46 am
Forum: Junior Level
Topic: MCQ highest
Replies: 3
Views: 2550

MCQ highest

A national math contest consisted of $11$ multiple choice questions, each having $11$ possible choices, of which only $1$ of the choices is correct. Suppose that $111$ students actually wrote the exam, and no two students have more than one answer in common. The highest possible average mark for the...