Question

1. У трикутнику АВС AB 8 см, см, BC = 9 CM, AL бісектриса трикутника. Знайдіть BL і LC.​

Answer 1

BL=4,5 см LC =4,5 см

Answer 2

Finding the Lengths BL and LC in Triangle ABC

To find the lengths BL and LC in triangle ABC, where AB = 8 cm, BC = 9 cm, and AL is the bisector of the triangle, we can use the angle bisector theorem.

The angle bisector theorem states that in a triangle, an angle bisector divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Using the Angle Bisector Theorem

Let's denote BL as x and LC as y. According to the angle bisector theorem:

AB/AC = BL/LC

Substituting the given values: 8/9 = x/y

Now, we can solve for x and y.

Solving for BL and LC

To find the values of BL and LC, we can use the given information and the angle bisector theorem.

Step 1: Set up the equation using the angle bisector theorem: 8/9 = x/y

Step 2: Solve for x and y: Cross-multiply to get: 8y = 9x

This equation represents the relationship between BL and LC.

Conclusion

Using the angle bisector theorem and the given information about the sides of triangle ABC, we have found that BL and LC are related by the equation 8y = 9x. This relationship allows us to determine the specific values of BL and LC in the triangle.