: E d+ Fd 2R
1. MOt s6 ban dd chira ,4P ld tluong tmng truc cila
doqnIJ. EC chung m:rr,hAP I1J, ngodi c6ch su dgng
dinh li Brocard, c6 th6 sir dpng b6 d6 sau:
Cho tam giac ABC, cac dwrtng cao BB', CC ' car nhau
rai H; F la gioo diem caa B'C'vrti BC. Khi dd FH 1.LP. 2. CAcbqnsau c6 loi giAi t6t hon c6. Hii Phdng: Zrorr-e Thd Son,l1 To6n, THPT chuydn TrAn Phri; Pht[ Thg:
Phqm Ngpc Hdi,10 Toitn, Vfi Thi Mai,l1 To6n 1.
THPT chuy6n Hiing Vucmg; NghQ An: Nguy€n Vdn
Huy,9D, THCS Li Nhpt Quang, D6 Lucrng, H6 Xudn
Hi.mg,l0Tl, THPT D6 Lucrng 1; Hi finh: Nguydn Vdn Th€, 10T1, Trdn Hdu Mqnh Cadng,1lT1, THPT
chuy6n Hd TTnh; Ninh Thuin: NSuyA, Trin LA Minh,
1 I To5n, THPT chuy6n L6 Quf Ddn.
HO QUANG VINH be a polynomial. Prove that there exists an integer a such thalJfu\ is divisibie by 3to'o'
Frotrlem Tl0 l-15. Does there exist a continuous
function/: R -+ R satisffing the followingproperty: for any x e IR, amongf.r), JU + I), property: for any x e IR, amongf.r), JU + I), /(x + 2) there are exaclty two rational numbers
and one irrational number?
Problem Tlll44s.Given a sequence {a, ii
where: ar: l, az-- 2014 and
2013a t - 2013\a--, n*t = r " +l \ l*-- n-ll . la- n-',. a--, n*t = r " +l \ l*-- n-ll . la- n-',.
Find tirnfl*l*...*l) for n : 2, 3, 4,...
,+-f a, a2 o,, )
Problem Tl2l445.Let ABCD be a quadrilateral circumscribing a circle (11. The sides ,48 and
BC are tangent to (I) at M andNrespectively' Let.E be the intersecnon of AC and MN, and F be the intersection of BC and DE. DMintersects
(I) at another point, say T. Prove that FZ is
tangent to (4.
Trans I at ed by NGUYEN PHU HOANG LAN m6t duong tron