Question

На отрезке AB длиной 24 см поставлены точки С и D так, что они оказались серединами некоторых из получившихся отрезков. Найти AC. Указать все возможные варианты.

Answer 1

С и Д делит отрезок АВ на три равные части. Точка С делит отрезок АД по полам АС=СД. Точка Д делит отрезок СВ на две равные части  СД=ДВ⇒     АС= СД = ДВ   
24:3=8 см. длина отрезка АС.

Answer 2

Answer in detail. On segment AB of length 24 cm, points C and D are placed so that they are the midpoints of some of the resulting segments. Find AC. Indicate all possible options.

There are two possible cases for this problem:

- Case 1: C is the midpoint of AB and D is the midpoint of BC (see figure below).

![Figure 1]

In this case, we can use the property of midpoints to find AC. Since C is the midpoint of AB, we have AC = CB = 24/2 = 12 cm. Since D is the midpoint of BC, we have BD = DC = 12/2 = 6 cm. Therefore, AC = 12 cm.

- Case 2: D is the midpoint of AB and C is the midpoint of AD (see figure below).

![Figure 2]

In this case, we can use the property of midpoints to find AC. Since D is the midpoint of AB, we have AD = DB = 24/2 = 12 cm. Since C is the midpoint of AD, we have AC = CD = 12/2 = 6 cm. Therefore, AC = 6 cm.

These are the only two possible cases for this problem. The answer is AC = 12 cm or AC = 6 cm.