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

by definition, an arc subtended by a central angle of some given measure has the same measure. so .