A circle with radius x is shown below. The diagram is not drawn to scale.
A circle is shown. A horizontal chord is drawn between the top and center of the circle. It is labeled 26. A line segment extends from the chord to the center. It is labeled 6. A small square is at the intersection of the chord and segment. A radius is drawn from the center to a point at the lower right on the circle. It is labeled x.
What is the value of x? Round the answer to the nearest tenth.
(1 point)
Responses
x = 20.0
x = 20.0
x = 25.3
x = 25.3
x = 14.3
x = 14.3
x = 26.7
To find the value of x, we can use the Pythagorean theorem since the chord is a diameter of the circle.
The chord (26) is the hypotenuse of a right triangle with legs of length 6 and x. Using the Pythagorean theorem:
x^2 = 26^2 - 6^2
x^2 = 676 - 36
x^2 = 640
x = sqrt(640)
x ≈ 25.3
Therefore, the value of x is x = 25.3, rounded to the nearest tenth.
The correct response is:
x = 25.3