Question

Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.

20
5
o
x
Оа
125
Ob
20.6
19.4
Od
11.2

Answer 1

11.2

Explanation:

x is the length of a radius of the circle, all radii have the same length.

the chord of length 20 is perpendicular to the segment of length 5, so the segment bisects the chord , so half of the chord is length 10.

The segment of length 10 is one leg of a right triangle while the segment of length 5 is the other leg. The hypotenuse is also a radius of the circle.

The length of the hypotenuse can be found by they Pythagorean Theorem, a^2 + b^2 = c^2, so

5^2 + 10^2 = c^2 or

25 + 100 = c^2 or

c^2 = 125 or

c =
`√(125)` = ≈ 11.2

so if one radius is approximately 11.2, then all radii (including the one of length x) are 11.2