Find the length of the unknown segment (x) in each figure. Use theorem of secant segment and external secant segment.

1. x = 6    2. x = 9   3. x = 3

Step-by-step explanation:

Use Intersecting Secants Theorem:

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

1.  AC and AD are secants that intersect at point A

So, AB x AC = AE x AD

          x 15 = 6 x (6 + 9)

             15 = 90

                  = 6

2.  KM and KN are secants that intersect at point K

So,  KL x KM = KO x KN

 10 x (10 + 8) = x 20

              180 = 20

                  = 9

3.  IG and IF are secants that intersect at point I

So,  IH x IG = IJ x IF

        x 39 = 9 x (9 + 4)

           39 = 117

                = 3

it would be:

c.parallelogram.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.