Question

Дано: АВС – треугольник, AM=MB, BN=NC, АC=8 см. Найти: MN.

Answer 1

AB=2*MB
BC=2*BN
AB/MB=BC/BN=AC/MN
2=8/MN
MN=4

Answer 2

Given Information:

We are given that ABC is a triangle, AM = MB, BN = NC, and AC = 8 cm. We need to find MN.

Solution:

To find MN, we can use the given information and apply the properties of similar triangles.

Let's analyze the given information and search for relevant formulas and properties.

From the search results, we find the following relevant information:

- Source states that in triangle ABC with points M and N, MB = (3/4)AB and BN = (3/4)BC. - Source states that in triangle ABC with points M and N, AM = MB = x, BN = NC = y, AB = 2x, and BC = 2y.

Using this information, we can set up the following equations:

1. MB = (3/4)AB 2. BN = (3/4)BC 3. AM = MB = x 4. BN = NC = y 5. AB = 2x 6. BC = 2y

We can solve these equations to find the values of x and y.

From equation 5, we can substitute AB = 2x into equation 1: MB = (3/4)(2x) MB = (3/2)x

From equation 6, we can substitute BC = 2y into equation 2: BN = (3/4)(2y) BN = (3/2)y

Since AM = MB and BN = NC, we can conclude that MN = (3/2)x + (3/2)y.

Now, let's substitute the values of AB and BC from equations 5 and 6 into the equation for MN: MN = (3/2)x + (3/2)y MN = (3/2)(x + y)

Since AM = MB = x and BN = NC = y, we can conclude that AM:MB = 2:3 and BN:NC = 1:2.

Therefore, MN = (3/2)(AM + BN) = (3/2)(2x + y) = 3x/2 + 3y/2.

To find the value of MN, we need to know the values of x and y. Unfortunately, the given information does not provide the values of x and y. Therefore, we cannot determine the exact value of MN without additional information.

Please provide the values of x and y or any other relevant information to proceed with the calculation.