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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.

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?Pa class=

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Given:

[tex]\begin{gathered} m\angle ACB=90 \\ \text{Diameter}=32 \end{gathered}[/tex][tex]\begin{gathered} \text{Radius}=\frac{\text{Diameter}}{2} \\ r=\frac{32}{2} \\ r=16 \end{gathered}[/tex][tex]\begin{gathered} AB=\frac{mAB}{360}\times2\pi r \\ AB=\frac{90}{360}\times2\pi(16) \\ AB=\frac{1}{4}\times32\pi \\ =8\pi \\ =25.132 \end{gathered}[/tex]

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