Answer:
x = 6
Step-by-step explanation:
Looking at the attached figure:
As the triangle ABC is inscribed inside the circle and AB is the diameter of the circle => ABC is the right triangle
So that ∡ACB = 90°
As ACB is the right triangle, according to the Pythagoras theorem, we have the formula as following:
[tex]AC^{2} +BC^{2} =AB^{2}[/tex]
=> [tex]BC^{2} = AB^{2} -AC^{2} = 20^{2} -16^{2} = 400-256= 144 = 12^{2}[/tex]
=> BC = 12
As O is the center of the circle
=> OA = 1/2 x AB = 1/2 x 20 = 10
Inside the triangle ABC, as OD is parallel with BC
=> AOD and ABC are similar triangles
=> [tex]\frac{OD}{BC} =\frac{AO}{AB}[/tex]
=> [tex]\frac{x}{12}=\frac{10}{20} =\frac{1}{2}[/tex]
=> x = 1/2 x 12 = 6
So x = 6
