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This problem is a checkpoint for solving problems involving circles, arcs, sectors, chords, and tangents.

It will be referred to as Checkpoint 12.

  1. In the figure at right, is the center of the circle. Calculate the value of and justify your answer.

Circle, with center point, labeled, O,  with 2 intersecting chords, with segments connecting the endpoints of each cord to create 2 triangles, with a common vertex, at the point of intersection. Angles labeled as follows: Left triangle, top inscribed angle, 12 degrees, angle left of intersection, 91 degrees. Right triangle, bottom inscribed angle, labeled, x.

  1. is the center of the circle and is tangent to the circle at point . If , calculate the area of the circle.

Circle with center labeled, c, points on the circle labeled, b, &, D, with point outside the circle, labeled, a, with segments from C, through, d, to, a, from, c, to, b, from, B, to, A, labeled, 24.

  1. Determine the value of .

Circle with 2 intersecting chords, creating 4 segments, labeled around the point of intersection as follows: top left, a, top right, 10, bottom right, 2, x, bottom left, 6.

Check your answers by referring to the Checkpoint 12 materials located at the back of your book.

Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that you need more confidence when solving these types of problems, then review the Checkpoint 12 materials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.

Answers and extra practice are located in the back of your printed textbook or in the Reference Tab of your eBook. If you have an eBook for Int2, login and then click the following link: Checkpoint 12: Circles, Arcs, Sectors, Chords, and Tangents