Question

В треугольнике ABC точки A1, B1 лежат соответственно на сторонах BC и AC. P - точка пересечения отрезков АА1 и ВВ1. найдите отношение :вроде можно решить через теорему чевы, но как хзДАЮ 84 БАЛЛА​

Answer 1

Ответ:

$\dfrac{BP}{PB_1}=\dfrac{45}{28}$

Объяснение:

Для треугольника ВВ₁С и секущей А₁А применим теорему Менелая:

$\dfrac{CA_1}{A_1B}\cdot \dfrac{BP}{PB_1}\cdot \dfrac{B_1A}{AC}=1$

По условию АВ₁ : В₁С = 7 : 8, значит В₁А : АС = 7 : 15.

$\dfrac{4}{3}\cdot\dfrac{BP}{PB_1}\cdot \dfrac{7}{15}=1$

$\dfrac{BP}{PB_1}\cdot \dfrac{28}{45}=1$

$\dfrac{BP}{PB_1}=\dfrac{45}{28}$

Answer 2

Finding the Ratio in Triangle ABC

To find the ratio in triangle ABC, where points A1 and B1 lie on sides BC and AC respectively, and P is the intersection point of segments AA1 and BB1, we can use the theorem of Ceva.

The theorem of Ceva states that in a triangle, if three cevians (lines that intersect a triangle's sides) are concurrent, then the ratio of the lengths of the segments they divide on each side is equal to the product of the ratios of the opposite sides.

Let's denote the lengths of the segments as follows: - AP = x - PA1 = y - BP = z - PB1 = w - A1C = m - BC = n - AC = p

According to the theorem of Ceva, we have the following equation:

x/y * w/z * m/n = 1

To find the ratio, we need to solve this equation. However, we don't have enough information about the lengths of the segments or the values of x, y, z, w, m, n, and p. Without this information, it is not possible to determine the exact ratio.

If you have additional information or specific values for the lengths of the segments or the variables, please provide them, and I will be happy to assist you further.