Question

17+9 б. Помогите решить, пожалуйста.Отрезок PK является биссектрисой треугольника POM. Найдите сторону OP, если MK = 8, OK = 6, MP = 12.Объясните решение, если не сложно. Заранее спасибо.

Answer 1

Решение приведено во вложении
биссектриса делит сторону на отрезки пропорциональные прилежащим сторонам, т.е.
РМ/РО=КМ/КО; 12/РО=8/6
РО=12·6/8=9
ответ 9

Answer 2

Problem Analysis

We are given that segment PK is the angle bisector of triangle POM. We need to find the length of segment OP, given that MK = 8, OK = 6, and MP = 12.

Solution

To solve this problem, we can use the Angle Bisector Theorem, which states that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

Let's denote the length of segment OP as x. According to the Angle Bisector Theorem, we can set up the following proportion:

MK / OK = MP / OP

Substituting the given values, we have:

8 / 6 = 12 / x

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

8x = 6 * 12

Simplifying further:

8x = 72

Dividing both sides by 8:

x = 9

Therefore, the length of segment OP is 9.

Conclusion

The length of segment OP is 9. This is found using the Angle Bisector Theorem, which states that the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides. In this case, we set up a proportion using the given lengths and solved for the unknown length of segment OP.