Question

BD биссектриса ΔАВС, АВ = 24 см, ВС = 20 см, AD на 3 см больше CD. Найти АС

Answer 1

Задача за 8 класс на свойство биссектрисы.

Answer 2

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Answer 3

Problem Statement

We are given triangle ABC with side lengths AB = 24 cm and BC = 20 cm. AD is 3 cm longer than CD. We need to find the length of AC.

Solution

To find the length of AC, we can use the angle bisector theorem. According to the theorem, the length of the angle bisector of a triangle is proportional to the lengths of the two sides that it divides.

Let's denote the length of AC as x. Since AD is 3 cm longer than CD, we can express AD as CD + 3.

Using the angle bisector theorem, we can set up the following proportion:

AC / AB = CD / BD

Substituting the given values, we have:

x / 24 = CD / BD

We also know that BD = BC + CD. Substituting the given values, we have:

BD = 20 + CD

Substituting this into the proportion, we have:

x / 24 = CD / (20 + CD)

To solve for x, we can cross-multiply and solve the resulting equation:

x * (20 + CD) = 24 * CD

Expanding and simplifying the equation, we have:

20x + x * CD = 24 * CD

Rearranging the equation, we have:

20x = 24 * CD - x * CD

Factoring out CD, we have:

20x = (24 - x) * CD

Dividing both sides by (24 - x), we have:

20x / (24 - x) = CD

Now, we can substitute the given values to find the length of CD. However, we don't have the exact values of CD and BD from the given information. Therefore, we cannot determine the exact length of AC without additional information.

Please provide the exact values of CD and BD or any other relevant information to solve the problem.