Question

Даю 70 баллов2. Паралельні прямі аib перетинають сторону ОА кута АОВ в точках N и C, а сторону OB в точках М і K, починаючи від вершини. Знайдіть довжину відрізка NC, якщо OM=3м, OK = 18м, ON=4м.​

Answer 1

Ответ:

20 м.

Объяснение:

За теоремою Фалеса про пропорційні відрізки:

ОМ/ОN=ОK/ОC

ОC=ОК*ОN:ОМ=18*4:3=24 м

NC=OC-ON=24-4=20 м.

Answer 2

To find the length of segment NC, we can use the concept of similar triangles. Let's break down the given information step by step.

Given: - OM = 3m - OK = 18m - ON = 4m

First, let's consider triangle OMK and triangle ONC. These triangles are similar because they have two pairs of congruent angles. The angle at O is common to both triangles, and the angles at M and N are congruent because they are vertical angles.

By the properties of similar triangles, we know that the corresponding sides of these triangles are proportional.

Let's consider the proportion of the corresponding sides:

OM/ON = OK/NC

Substituting the given values, we have:

3/4 = 18/NC

To find the value of NC, we can cross-multiply and solve for NC:

3 * NC = 4 * 18

3NC = 72

NC = 72/3

NC = 24m

Therefore, the length of segment NC is 24 meters.