Question

1. On a circle with center O, chord AB connects points A and B on the circle and measures

17.5 inches. The circle also has a radius measuring12 inches.
1.a. Draw a diagram of the circle. Be sure to label points A, B and O.
1.b. Find the length of ARC AB
1.c. Find the area of sector OAB.

Answer 1

To find the length of arc AB, use the formula: Length of arc = (Central angle / 360) * Circumference. To find the area of sector OAB, use the formula: Area of sector = (Central angle / 360) * Π * (Radius squared).

Step-by-step explanation:

To draw a diagram of the circle, place point O in the center. Label points A and B on the circumference. The length of AB is 17.5 inches. The radius of the circle is 12 inches.

To find the length of arc AB:

1. Use the formula: Length of arc = (Central angle / 360) * Circumference
2. Find the central angle: central angle = (Length of chord / Diameter) * 360
3. The diameter is twice the radius, so it is 2 * 12 inches = 24 inches.
4. Substituting the values, central angle = (17.5 inches / 24 inches) * 360 = 262.5 degrees
5. Plug the central angle into the formula for length of arc: length of arc AB = (262.5 degrees / 360) * Π * Diameter

To find the area of sector OAB:

1. Use the formula: Area of sector = (Central angle / 360) * Π * (Radius squared)
2. Substituting the values, area of sector OAB = (262.5 degrees / 360) * Π * (12 inches) squared

Learn more about Circle measurements