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
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 \(BD⊥BC\)
Let P be the intersection point of 3 internal bisectrices of a given triangle ABC. The line passing through P and perpendicular to CP intersects AC and BC at M and N. If AP=3cm, BP=4cm, compute AM/BN?
Ta có
\(\widehat{ABM}=\widehat{APC}-\widehat{MPC}=\left(90+\frac{\widehat{ABC}}{2}\right)-90=\widehat{PBC}\)
Tương tự tra có: \(\widehat{NPB}=\widehat{PAM}\)
\(\Rightarrow\Delta MAP\approx\Delta NPB\)
\(\Rightarrow\frac{AP}{PB}=\frac{MA}{NP}=\frac{MP}{NB}\)
\(\Rightarrow MA.NB=NP.MP=NP^2=MP^2\)(Dễ thấy tam giác MNC cân có CP là đường cao và đường phân giác)
Ta lại có: \(\frac{MA}{NB}=\frac{MA^2}{MA.NB}=\frac{MA^2}{NP^2}=\frac{AP^2}{PB^2}=\frac{3^2}{4^2}=\frac{9}{16}\)
The area of a triangle ABC is , take the point M on BC such that BM=MC and the point N on AC such that AN=NC. Find the area of the triangle AMN
nhanh nhé, mk tick cho
Tự vẽ hình nha.
Diện tích tam giác AMC là:
240 :2=120 (đv diện tích)
Diện tích tam giác AMN là:
120;2 = 60 ( đv diện tích )
Đáp số: 60
Let ABCD be a trapezoid with bases AB, CD and O be the intersection of AC and BD. If the areas of triangle OAB, triangle OCD are 16cm2, 40cm2respectively and M is the midpoint of BD, then the area of the triangle AMD is .........cm2.
Let ABCD be a trapezoid with bases AB, CD and O be the intersection of AC and BD. If the areas of triangle OAB, triangle OCD are 16cm2, 40cm2respectively and M is the midpoint of BD, then the area of the triangle AMD is .........cm2.
đựng đường cao 2 bên áp dụng 2 tam giác đồng dạng suy ra tỉ số diện tích
đáp án 22 cm2
Let ABC be an isoceles triangle (AB = AC) and its area is 501cm2. BD is the internal bisector of the angle ABC (D ∈ AC), E is a point on the opposite ray of CA such that CE = CB. I is a point on BC such that CI = 1/2 BI. The line EI meets AB at K, BD meets KC at H. Find the area of the triangle AHC.
bái phục giờ vẫn còn thi toán tiếng anh á ghê á nha
thi xog cấp tỉnh là vứt luôn nhác thi lắm luôn
Given the triangle ABC with median AM, AB=5cm, AC=12cm.
a) Calculate the lengths of BC, AM
b) D for the point symmetric to A with respect to M. Prove AD=BC and calculate the area of ABCD
c) For what condition of right triangle ABC does ABCD become a square?
