Let M be a point inside the rectangle ABCD. Suppose that and
. Find the value of
.
Answer:
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1. Two bisector BD and CE of the triangle ABC intersect at O. Suppose that BD.CE 2BO.OC . Denote by H the point in BC such that .OH⊥BC . Prove that AB.AC 2HB.HC 2. Given a trapezoid ABCD with the based edges BC3cm , DA6cm ( AD//BC ). Then the length of the line EF ( Ein AB,Fin CD and EF // AD ) through the intersection point M of AC and BD is ............... ? 3. Let ABC be an equilateral triangle and a point M inside the triangle such that MA^2MB^2+MC^2 . Draw an equilateral triangle ACD whe...
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1. Two bisector BD and CE of the triangle ABC intersect at O. Suppose that BD.CE = 2BO.OC . Denote by H the point in BC such that .\(OH⊥BC\) . Prove that AB.AC = 2HB.HC
2. Given a trapezoid ABCD with the based edges BC=3cm , DA=6cm ( AD//BC ). Then the length of the line EF ( \(E\in AB,F\in CD\) and EF // AD ) through the intersection point M of AC and BD is ............... ?
3. Let ABC be an equilateral triangle and a point M inside the triangle such that \(MA^2=MB^2+MC^2\) . Draw an equilateral triangle ACD where \(D\ne B\) . Let the point N inside \(\Delta ACD\) such that AMN is an equilateral triangle. Determine \(\widehat{BMC}\) ?
4. Given an isosceles triangle ABC at A. Draw ray Cx being perpendicular to CA, BE perpendicular to Cx \(\left(E\in Cx\right)\) . Let M be the midpoint of BE, and D be the intersection point of AM and Cx. Prove that \(BD⊥BC\)
I is a point inside the rectangle ABCD. IA = 13 cm, IB = 8 cm and IC = 4 cm. Find ID
Bài 2
Quy ước: tất cả đều viết véc tơ:
* Khai thác giả thiết:
+ IA =2IB <=> IA = 2( AB -AI) <=> IA = -2AB <=> AI = 2AB
+ 3JA + 2JC =0 <=> 3JA + 2(JA+ AC) =0 <=> JA = ( -2/5)AC <=> AJ = (2/5) AC
Chỉ ra được vị trí các điểm I, J:
+ I đối xứng với A qua B ( tức B là trung điểm AI)
+ J nằm trên đoạn AC sao cho AJ = 2/5 AC
* Ta có:
+ GI = GA + AI = GA + 2AB
+ GJ = GA + AJ = GA + (2/5) AC
Suy ra:
GI - 5 GJ = -4 GA + 2(AB - AC) = -4GA + 2CB = -4GA + 2(GB -GC)
= -2GA +4GB ( chỗ này có áp dụng tính chất trọng tâm: GA +GB + GC =0)
Do B là trung điểm của AI => 2GB = GA +GI
Suy ra:
GI - 5 GJ = -2GA + 2GA + 2 GI
=> GI = - 5 GJ
Đẳng thức này suy ra I, J, G thẳng hàng => IJ đi qua G (đpcm)
I is a point inside the rectangle ABCD. IA = 13 cm, IB = 8 cm and IC = 4 cm. Find ID
The area of a rectangle ABCD is 56cm2. Given a random point E inside of ABCD.Find the total area of triangles AED and BEC.
In rectangle ABCD, AC = BD, HI = AB
We have: S"AED" + S"BEC"
= AC x HE : 2 + BD x EI : 2
AC = BD so AC x HE : 2 + AC x EI : 2
= AC x (HE + EI) : 2
= AC x HI : 2
= AC x AB : 2
Area of this rectangle is 56cm2, or AC x AB, so:
= 56 cm2 : 2
= 28 cm2
Result: 28 cm2
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Giải ngay ! Gải nhanh ! Giải đúng !Number 2 : The area of a rectangle ABCD is 56cm2. Given a random point E inside of ABCD. Find the total area of triangles AED and BEC. Answer: ............. cm2.Number 3 :Peter and Jacob were running. Both of them run with their constant speeds. They started at the same time and the same place. When Jacob reached the finishing line, Peter had only run 5/8 of what Jacob had run. Jacob’s speed is 75m/min (metre per minute) faster than Peter. What was Peter’s spe...
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Giải ngay ! Gải nhanh ! Giải đúng !
Number 2 : The area of a rectangle ABCD is 56cm2. Given a random point E inside of ABCD. Find the total area of triangles AED and BEC.
Answer: ............. cm2.
Number 3 :Peter and Jacob were running. Both of them run with their constant speeds. They started at the same time and the same place. When Jacob reached the finishing line, Peter had only run 5/8 of what Jacob had run. Jacob’s speed is 75m/min (metre per minute) faster than Peter. What was Peter’s speed in m/min?
Answer: ............. m/min.
I is a point inside the rectangle ABCD. IA=13cm, IB=8 cm, IC=4 cm. Find ID
mình dịch ra cho:cho hình chữ nhật abcd và có điểm I nằm trong hình chữ nhật ấy sao cho ia=13, ib=8, ic=4 tính id
mình mới lớp 7 thôi nên không biết làm
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nâng cao và phát triển toán 8 tập 1 bài 71.Áp dụng vào làm
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I is a point inside the rectangle ABCD. IA=13cm, IB=8 cm, IC=4 cm. Find ID
ta có \(AB^2=CD^2\Leftrightarrow IA^2+IB^2=ID^2+IC^2\)
Thay số vào ta tính được \(ID=\sqrt{217}\)
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Given a segment AB = 100cm. Let C be a point between A and B. Let M, N be respectively the midpoint of the segment BC, AC. Find the length of the segment MN.
Given a segment AB = 100cm. Let C be a point between A and B. Let M, N be respectively the midpoint of the segment BC, AC. Find the length of the segment MN.
Answer : MN = 50 cm
P/s : k mình nha bạn
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Given the Triangle ABC and the point M inside the triangle (M don't belong on any sides of triangle).let I be the intersection point of the line BM and the side AC
a, compare MA to MI+MB,then prove that MA +MB<IB+IA
b, compare IB to IC+CB, then prove that IB+IA<CA+CB
c, Demonstrate the inequality MA+MB<CA+CB