Question

13.
what is the value of x to the nearest tenth?
○ 26.8
○ 30.0

Explanation:

Step1: Identify the right triangle

We have a right triangle with hypotenuse 18 (radius of the circle) and one leg 12. Let the other leg (half of the chord) be \( y \). Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( c = 18 \) and \( b = 12 \), we solve for \( y \).

$$ y^2 + 12^2 = 18^2 $$

$$ y^2 + 144 = 324 $$

$$ y^2 = 324 - 144 $$

$$ y^2 = 180 $$

$$ y = \sqrt{180} $$

Step2: Find the length of the chord \( x \)

Since the perpendicular from the center to a chord bisects the chord, \( x = 2y \).

$$ x = 2\sqrt{180} $$

$$ x = 2\times13.4164 $$

$$ x \approx 26.8 $$

Answer:

26.8