## Search found 550 matches

Fri May 10, 2013 12:59 am
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2013 Problem 5
Replies: 1
Views: 2458

(I got the idea to use Harmonic Division in this problem from Nadim Ul Abrar vai after the exam. This problem actually made me learn Harmonic Division) Let $BR\cap \omega=E', CE'\cap AR=S$. Now by the first lemma of Zhao, $AC$ is a symmedian of $\triangle ABD$. Thus $(C,A;D,B)=-1$. Thus $E'(C,A;D,B)... Fri May 10, 2013 12:15 am Forum: Asian Pacific Math Olympiad (APMO) Topic: APMO 2013 Problem 3 Replies: 2 Views: 2557 ### Re: APMO 2013 Problem 3 (This is a solution I saw later in the math camp.) Let$\displaystyle\sum_{i=1}^{k}a_i=A,\displaystyle\sum_{i=1}^{k}b_i=B$. Also let$X_i=X_1+(i-1)d$. Since$X_1,X_2$are integers,$d=X_2-X_1$is also an integer. Then,$\displaystyle\sum_{i=1}^{k}(a_in+b_i+1)>\displaystyle\sum_{i=1}^{k}\lfloor a_in+...
Thu May 09, 2013 11:47 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 2013 Problem 2
Replies: 1
Views: 1873