Search found 14 matches
- Fri May 07, 2021 9:34 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 9
- Replies: 7
- Views: 14549
Re: BdMO National 2013: Junior 9
In 2 numbers GCD their common factor remains multiple of those numbers and in LCM it remains with the common factors and other factors remains multiple. So in the ratio of GCD and LCM common factors cancel out and remains the others factors without those common factors. Now, 36=2×2×3×3 these 4 facto...
- Thu Apr 29, 2021 7:35 pm
- Forum: National Math Camp
- Topic: AIME
- Replies: 2
- Views: 50560
AIME
Peter, Paul, David join a table tennis tournament. On the first day, two of them were randomly chosen to play a game against each other. On each subsequent day, the loser of the game on the previous day would be benched and the other two would play a game. After a certain number of days, it was foun...
- Mon Apr 26, 2021 10:30 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Primary Category Problem 9
- Replies: 1
- Views: 4475
Re: BdMO National 2021 Primary Category Problem 9
DEF triangles DF segment has the equal length of the shaded regions 3 segments and other 3 segments has the equal length of ABC triangles AC segment
Shaded regions perimeter = $\frac{12}{3}$ + $\frac{15}{3}$ = 9
Shaded regions perimeter = $\frac{12}{3}$ + $\frac{15}{3}$ = 9
- Mon Apr 26, 2021 8:20 am
- Forum: National Math Camp
- Topic: AIME P4
- Replies: 4
- Views: 6440
Re: AIME P4
[attachment=0]20210426_081732.jpg[/attachment]
- Sun Apr 25, 2021 4:47 pm
- Forum: National Math Camp
- Topic: AIME P4
- Replies: 4
- Views: 6440
Re: AIME P4
2018
- Sat Apr 24, 2021 12:55 pm
- Forum: National Math Camp
- Topic: AIME P4
- Replies: 4
- Views: 6440
AIME P4
Let x, y, z be nonnegative numbers x² + y² + z² + x + 2y + 3z = $\frac{13}{4}$
. Find
the minimum value of x + y + z
. Find
the minimum value of x + y + z
- Wed Apr 21, 2021 10:45 pm
- Forum: National Math Camp
- Topic: Geomock
- Replies: 0
- Views: 5731
Geomock
In acute ∆ABC, let AD be the altitude from A on BC. Let P be a point on
AD. Line P B meets AC at E and P C meets AB at F. Suppose that AEDF is concyclic. Prove
that $\frac{P A}{P D}$ = (tanB + tanC)cot($\frac{A}{2}$)
AD. Line P B meets AC at E and P C meets AB at F. Suppose that AEDF is concyclic. Prove
that $\frac{P A}{P D}$ = (tanB + tanC)cot($\frac{A}{2}$)
- Wed Apr 21, 2021 8:16 am
- Forum: National Math Camp
- Topic: National Camp Exam 2018 P3
- Replies: 4
- Views: 5819
Re: National Camp Exam 2018 P3
You did the summation of infinite series?
- Tue Apr 20, 2021 9:27 pm
- Forum: National Math Camp
- Topic: National Camp Exam 2018 P3
- Replies: 4
- Views: 5819
National Camp Exam 2018 P3
Find x=$\sqrt[]{1+1/1²+1/2²}$ +$\sqrt[]{1+1/2²+1/3²}$...+$\sqrt[]{1+1/2012²+1/2013²}$
- Tue Apr 20, 2021 8:57 pm
- Forum: National Math Camp
- Topic: National Camp Exam 2018 P9
- Replies: 1
- Views: 1934
National Camp Exam 2018 P9
The equation \begin{align*}
9x³-3x²-3x-1 & =0
\end{align*} has a real root of the form $\frac{√3a+√3b+1}{c}$
where
a, b, c are positive integers. Find a + b + c.
9x³-3x²-3x-1 & =0
\end{align*} has a real root of the form $\frac{√3a+√3b+1}{c}$
where
a, b, c are positive integers. Find a + b + c.