Дано: AC : BC = 3 : 2, CC’ = 10 cm
Let’s denote the length of BC as x. Since AC : BC = 3 : 2, we can write AC = 3x and BC = 2x.
Using the given information that CC’ = 10 cm, we can now find the length of BC’.
Since the line BC’ is parallel to AB, we can use the intercept theorem to find the length of BC’.
The intercept theorem states that if two parallel lines are intersected by a transversal, then the ratio of the lengths of the segments intercepted on the parallel lines is equal.
In our case, AB is the transversal intersecting parallel lines BC and BC’. The ratio of the lengths of the segments intercepted on the parallel lines is given by AC’ : CC’.
Since AC’ = AC = 3x, the ratio AC’ : CC’ can be written as 3x : 10.
Therefore, 3x : 10 = AC : CC’, which gives us 3x : 10 = 3x : 10.
This means that BC’ = BC = 2x.
Now we can find the length of segment BB’.
Since BB’ is the sum of BC and BC’, we have BB’ = BC + BC’ = 2x + 2x = 4x.
Therefore, the length of segment BB’ is 4x.
So, to find the length of segment BB’, we need to find the value of x.
We know that AC : BC = 3 : 2, which can be written as 3x : 2x = 3 : 2.
Simplifying this ratio, we get 3x = 2(2x).
Solving this equation, we find x = 0.
Since x = 0, it means that the lengths of BC and BB’ are also 0.
Therefore, the length of segment BB’ is 0 cm.