Answer:
[tex]a)\ \ 4[/tex]
Step-by-step explanation:
A secant is a line that intersects a circle in two points. The product of the lengths theorem is a theorem that forms a ratio between the lengths of the secants when two secants intersect in a circle. Let ([tex]secant_1[/tex]) and ([tex]secant_2[/tex]) refer to the entirety of the secants. ([tex]part_1_a[/tex]) and ([tex]part_1_b[/tex]) will refer to the different parts of ([tex]secant_1[/tex]). ([tex]part_2_a[/tex]) and ([tex]part_2_b[/tex]) will refer to the different parts of ([tex]secant_2[/tex]).
[tex]part_1_a*part_1_b=part_2_a*part_2_b[/tex]
Substitute with the given values in the problem,[tex]part_1_a*part_1_b=part_2_a*part_2_b[/tex]
[tex]x*9=3*12[/tex]
Simplify,
[tex]x*9=3*12[/tex]
[tex]9x=36[/tex]
Inverse operations,
[tex]9x=36[/tex]
[tex]x=4[/tex]
