cho hinh vuong ABCD. Qua A ve hai duong thang vuong goc voi nhau lan luot cat BC tai P va R, cat Cd tai Q va S.

a, chung minh tam giac AQR va tam giac APS la cac tam giac can

b, QR cat PS tai H; M,N la trung diem cua QR va PS. chung minh tu giac AMHN la hinh chu nhat

c, chung minh P la truc tam

d, chung minh MN la duong trung truc cua AC

e, chung minh bon diem M, B,N,D thang han

cho tam giac ABC co ba goc nhon, cac duong cao BD,CE cat nhau tai H.

a, chung minh ΔABD giao ΔACE

b, chung minh BH.HD=CH.HE

c, Noi D voi E cho biet BC=a,AB=AC=b. tinh do dai doan thang DE theo a

cho x,y,z la cac so nguyen duong thoa man \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=2015\)

tinh gia tri lon nhat cua bieu thuc P=\(\dfrac{xy}{x^3+y^3}+\dfrac{yz}{y^3+z^3}+\dfrac{zx}{z^{3+x^3}}\)