Question

circle has center C, as shown below, and diameter 32 cm. Find the length of AB if m∠ABC = 90°Part I: What fractional part of the circle's circumference is AB?Part II: Use the fraction you determined in Part I and the circumference formula to find the length of AB. Show your work and round your answer to the nearest hundredth.

Answer 1

Given:

`\begin{gathered} m\angle ACB=90 \\ \text{Diameter}=32 \end{gathered}`
`\begin{gathered} \text{Radius}=\frac{\text{Diameter}}{2} \\ r=(32)/(2) \\ r=16 \end{gathered}`
`\begin{gathered} AB=(mAB)/(360)*2\pi r \\ AB=(90)/(360)*2\pi(16) \\ AB=(1)/(4)*32\pi \\ =8\pi \\ =25.132 \end{gathered}`