Question

В треугольнике ACD проаелина биссектриса DK найдите длину стороны CD если AD=16 Ak=8 CK=6 Помогите пожалуйста очень сильно прошу

Answer 1

Биссектриса делит противолежащую сторону пропорционально прилежащим сторонам
AD/AK = CD/CK
16/8 = CD/6
2 = CD/6
CD = 2*6 = 12

Answer 2

Calculation of CD in Triangle ACD

To find the length of side CD in triangle ACD, we can use the angle bisector theorem. According to the theorem, the length of side CD can be determined by the ratio of the lengths of the other two sides, AD and AK, multiplied by the ratio of the lengths of the angle bisector DK and CK.

Given: - AD = 16 - AK = 8 - CK = 6

Let's calculate the length of CD using the angle bisector theorem.

The angle bisector theorem states that the ratio of the lengths of the sides of a triangle is equal to the ratio of the lengths of the segments created by the angle bisector.

In triangle ACD, the angle bisector DK divides side AC into segments AK and CK. The ratio of the lengths of these segments is equal to the ratio of the lengths of the other two sides, AD and CD.

Using the angle bisector theorem, we can write:

AK/CK = AD/CD

Substituting the given values:

8/6 = 16/CD

Cross-multiplying:

8 * CD = 6 * 16

Simplifying:

8 * CD = 96

Dividing both sides by 8:

CD = 96/8

Calculating:

CD = 12

Therefore, the length of side CD in triangle ACD is 12 units.

Please let me know if you need any further assistance!