For the following question, what is the value of x to the nearest tenth?
A circle with a radius labeled x contains a chord labeled 11. The chord has a perpendicular line labeled 3 point 6 that intersects the center point of the circle.
(1 point)
Responses
4.2
4.2
6.6
6.6
10.4
10.4
11.6
To solve this question, we can use the properties of a circle.
First, we can draw a radius from the center of the circle to the chord. This creates a right triangle with the chord as the hypotenuse and the radius as one of the legs.
The other leg of the right triangle is the perpendicular line labeled 3.6.
Using the Pythagorean Theorem, we can find the length of the radius:
(radius)^2 + (3.6)^2 = (11)^2
(radius)^2 + 12.96 = 121
(radius)^2 = 121 - 12.96
(radius)^2 = 108.04
radius ≈ √(108.04)
radius ≈ 10.4
Therefore, the value of x, which represents the radius, to the nearest tenth is 10.4.