Question

Медианы АМ, ВТ и СК треугольника АВС пересекаются в точке О. Известно, что АО = 6 см, ВО = 10 см, КО = 4 см. Найдите медианы треугольника АВС. Можно ответ..

Answer 1

AO/AM  BO/BT  KO/CK = 1/2

6/3 = 2 10/3=3.3 4/3=0.5

2+6=8 3.3+10=13.3 4+0.5=4.5

Answer 2

Finding the Medians of Triangle ABC

To find the medians of triangle ABC, we need to determine the lengths of the medians. The medians of a triangle are the line segments that connect each vertex to the midpoint of the opposite side.

Given that AO = 6 cm, BO = 10 cm, and CO = 4 cm, we can use the properties of medians to find the lengths of the medians.

Let's denote the medians as AD, BE, and CF, where D is the midpoint of BC, E is the midpoint of AC, and F is the midpoint of AB.

To find the length of AD, we can use the fact that the medians of a triangle divide each other in a 2:1 ratio. This means that the length of AD is twice the length of OD.

Since OD is half of BO, we can calculate the length of AD as follows:

AD = 2 * OD = 2 * (1/2) * BO = BO

Therefore, the length of AD is 10 cm.

Similarly, we can find the lengths of BE and CF using the same logic.

BE = 2 * OE = 2 * (1/2) * AO = AO = 6 cm

CF = 2 * OF = 2 * (1/2) * CO = CO = 4 cm

Therefore, the lengths of the medians of triangle ABC are:

AD = 10 cm

BE = 6 cm

CF = 4 cm

Please let me know if you need any further assistance!