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Find the value of z.

 

 Apr 17, 2020
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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

 Apr 17, 2020

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