Search found 172 matches

by Zzzz
Sun Feb 12, 2012 9:11 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 5
Replies: 5
Views: 3397

BdMO National 2012: Junior 5

Problem 5: $ABC$ is a right triangle with hypotenuse $AC$. $D$ is the midpoint of $AC$. $E$ is a point on the extension of $BD$. The perpendicular drawn on $BC$ from $E$ intersects $AC$ at $F$ and $BC$ at $G.$ (a) Prove that, if $DEF$ is an equilateral triangle then $\angle ACB = 30^0$. (b) Prove t...
by Zzzz
Sun Feb 12, 2012 9:09 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 4, Primary 8
Replies: 8
Views: 3746

BdMO National 2012: Junior 4, Primary 8

Problem 4: A magic box takes two numbers. If we can obtain the first number by multiplying the second number with itself several times then a green light on the box turns on. Otherwise, a red light turns on. For example, if you enter $16$ and $2$ then the green light turns on because $2×2× 2×2 = 16...
by Zzzz
Sun Feb 12, 2012 9:05 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Junior 2, Primary 3
Replies: 2
Views: 2286

BdMO National 2012: Junior 2, Primary 3

Problem:
Prove that, the difference between two prime numbers larger than $2$ can’t be a prime number other than $2$.
by Zzzz
Sun Feb 12, 2012 8:55 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 9
Replies: 6
Views: 3545

BdMO National 2012: Secondary 9

Problem 9:
Consider a $n×n$ grid of points. Prove that no matter how we choose $2n-1$ points from these, there will always be a right triangle with vertices among these $2n-1$ points.
by Zzzz
Sun Feb 12, 2012 8:51 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 8
Replies: 10
Views: 4950

BdMO National 2012: Secondary 8

Problem 8: The vertices of a right triangle $ABC$ inscribed in a circle divide the circumference into three arcs. The right angle is at $A$, so that the opposite arc $BC$ is a semicircle while arc $AB$ and arc $AC$ are supplementary. To each of the three arcs, we draw a tangent such that its point ...
by Zzzz
Sun Feb 12, 2012 8:48 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 4, Junior 8
Replies: 3
Views: 2289

BdMO National 2012: Secondary 4, Junior 8

Problem:
Find the total number of the triangles whose all the sides are integer and longest side is of $100$ in length. If the similar clause is applied for the isosceles triangle then what will be the total number of triangles?
by Zzzz
Sun Feb 12, 2012 8:46 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National 2012: Secondary 2, Junior 3, Primary 7
Replies: 7
Views: 3921

BdMO National 2012: Secondary 2, Junior 3, Primary 7

Problem : When Tanvir climbed the Tajingdong mountain, on his way to the top he saw it was raining $11$ times. At Tajindong, on a rainy day, it rains either in the morning or in the afternoon; but it never rains twice in the same day. On his way, Tanvir spent $16$ mornings and $13$ afternoons witho...
by Zzzz
Tue Jan 31, 2012 11:04 am
Forum: Algebra
Topic: Functional equation
Replies: 10
Views: 3796

Re: Functional equation

Am I missing something? :?

What about this one? $f(x)= \frac{1}{2} + \frac{\sqrt{2}}{4},\ \ \forall x$
by Zzzz
Tue Jan 31, 2012 10:33 am
Forum: Algebra
Topic: Functional equation
Replies: 10
Views: 3796

Re: Functional equation

such 'a' function or 'all' functions...?
by Zzzz
Fri May 27, 2011 7:27 am
Forum: Secondary Level
Topic: sin s are rational, so..cos s are rational
Replies: 1
Views: 1257

sin s are rational, so..cos s are rational

$sin\ A,sin\ B,sin\ C$ of a triangle are rational. Prove that $cos\ A,cos\ B,cos\ C$ are also rational.