Question

the circle shown has a diameter of 40 centimeters. the length of rc is 12 centimeters, and the length of uv is 16 centimeters.
determine the length of cu.
enter the answer in the space provided. use numbers instead of words.
cm

Explanation:

Step1: Find the radius of the circle

The diameter of the circle is 40 cm, so the radius \( r = \frac{40}{2} = 20 \) cm.

Step2: Recognize the right triangle

Since \( CU \) is perpendicular to \( UV \), triangle \( CUV \) is a right triangle with hypotenuse \( CV \) (which is the radius, 20 cm) and one leg \( UV = 16 \) cm. Let \( CU = x \).

Step3: Apply the Pythagorean theorem

In a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a, b \) are the legs. So \( x^2 + 16^2 = 20^2 \).

Step4: Solve for \( x \)

\( x^2 = 20^2 - 16^2 = 400 - 256 = 144 \). Then \( x = \sqrt{144} = 12 \).

Answer:

12