Question

Find the value of x. The dot represents the center of the circle, 20 represents the length of the diameter, and 16 is the length of the chord.
picture is attached​

Answer 1

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:

    $AC^{2} +BC^{2} =AB^{2}$

=> $BC^{2} = AB^{2} -AC^{2} = 20^{2} -16^{2} = 400-256= 144 = 12^{2}$

=> 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

=> $\frac{OD}{BC} =\frac{AO}{AB}$

=> $\frac{x}{12}=\frac{10}{20} =\frac{1}{2}$

=> x = 1/2 x 12 = 6

So x = 6