+499 We can make use of the power of a point theorem, a useful application for geometry.
It has 3 variations, and in this case, I'll use 1 of them : the case with two secants intersecting a circle(in other words, the lines intersect the circle at two points each).
It states:
Given the two secants in this problem GJ and GL,
GH * GJ = GK * GL
we are given that:
GH = 13
GJ = z + 13
GK = 9
GL = 39
Substituting, we get:
13(z+13) = 9 * 39
Dividing by 13 on both sides, we get:
z+ 13 = 9 * 3
z + 13 = 27
z = 14
