In triangle ABC the points D and E are the intersections of the angular bisectors from C and B with the sides AB and AC respectively. Points F and G on the extentions of AB and AC beyond B and C respectively, satisfy BF= CG= BC. Prove that FG//DE.
Let a,b be the roots of equation \(x^2-px+q=0\) and let c,d be the roots of the equation \(x^2-rx+s=0\), where p,q,r,s are some positive real numbers. Suppose that :
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}\)
is an integer. Determine a,b,c,d .
find the value of n such that the polynomial 2x^5 - 3x^3 + x^2 +n is divisible by the polynomial x+2
Let M be a point inside the rectangle ABCD. Suppose that and . Find the value of .
Answer:
Cho ∆ABC vuông tại A ( AB < AC ), vẽ đường cao AH ( H thuộc BC )
a) CM : ∆ABH ~ ∆ABC, từ đó suy ra BA2 = BH.BC
b) CM : AH2 = HB.HC
c) Lấy 2 điểm M, N thuộc cạnh AB, AC sao cho AM = 1/3AB, CN = 1/3AC. Chứng minh : ∆MHN vuông tại H
d) Cho AB = 6cm, AC = 8cm. Vẽ đường phân giác AD của góc BAC ( D thuộc BC ). Tính độ dài BD
(●´∀`●) Giúp tớ giải câu c, d nha (●´∀`●)
cho tam giac abc,d thuoc bc.ve diem e doi xung voi d qua ab,ve diem f dôi xung voi d qua ac a)chung minh rang:ae=à b)tam giac abc co them dieu kien gi de e doi xung voi f qua a
let a<b<c<d be integers. If one of the roots pf the equation (x-a)(x-b)(x-c)(x-d) - 9 is x=7, what is a+b+c+d?
cho tam giac abc,d thuoc bc.ve diem e doi xung voi d qua ab,ve diem f dôi xung voi d qua ac:
a)chung minh rang:ae=af
b)tam giac abc co them dieu kien gi de e doi xung voi f qua a
Các bn ơi giúp mk với!!!!!!
From 0,1,2,3,4 and 5, we choose two different number x and y . what is the largest possible value of \(2\left(x+y\right)^2+\left(x-y\right)^2\)