Given: FG (SEG) bisects BT (SEG)

BO=7x-6
OT=5x+10

Prove: BO=50

There appears to be insufficient information. Where is O, with respect to BT and FG?

It appears to me that O is midway between B and T. If so, then

7x-6 = 5x+10
2x = 16
x = 8

So, BO = 5*8+10 = 50

To prove that BO is equal to 50, we need to use the given information and solve for the value of x. Let's break down the given information step by step:

1. FG (SEG) bisects BT (SEG): This means that the line segment FG divides the line segment BT into two equal parts. Let's call the point of intersection between FG and BT as I.

2. BO = 7x - 6: This equation represents the length of the segment BO.

3. OT = 5x + 10: This equation represents the length of the segment OT.

Now, since FG bisects BT, it means that BI is equal to IT. In other words, the length of the segment BO plus the length of the segment OT should be equal to the length of the segment BT. We can write this as an equation:

BO + OT = BT

Substituting the given values, we have:

(7x - 6) + (5x + 10) = BT

Combining like terms:

12x + 4 = BT

Since FG bisects BT, the length of BT is divided into two equal parts. So, BT = 2BI. Substituting this into the equation, we have:

12x + 4 = 2BI

But we know that BI is equal to IT from the given information, so IT is equal to (5x + 10):

12x + 4 = 2(5x + 10)

Simplifying:

12x + 4 = 10x + 20

Subtracting 10x from both sides:

2x + 4 = 20

Subtracting 4 from both sides:

2x = 16

Dividing both sides by 2:

x = 8

Now that we have found the value of x, we can substitute it back into the equation for BO to find its value:

BO = 7x - 6 = 7(8) - 6 = 56 - 6 = 50

Therefore, we have proven that BO equals 50.