There is a theorem in Geometry that states that the product of one secant segment and its exterior segment equals the product of the other secant segment (in the same circle) and its exterior segment. In other words, LN x MN would half to equal PN x ON. With this equation in mind, all we have to do is substitute the lengths of the segments listed above.
(LN)(MN) = (PN)(ON)
(15 + 3)(3) = (x + 2)(2)
(18)(3) = (x + 2)(2)
54 = 2x + 4
50 = 2x
25 = x
Final Answer: x = 25
