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Home > CCG > Chapter 12 > Lesson 12.1.4 > Problem 12-52

12-52.

Use the relationships in each diagram below to solve for the given variables.  

  1. A circle with a secant line and a tangent line which meet outside the circle. The inner arc is 87 degrees and the outer arc is 153 degrees.

    The secant-tangent angle is half the difference between the major and minor arcs.

    The total measure of all the arcs in a circle is 360°.

  1. The area of is sq. units.
    A tangent line to a circle, center, K, is labeled, S, at the point of tangency. A extended line segment from, K through the circle at an angle meets the tangent line at, T. S, T is 8. Angle S, T, K, is, a. The distance from, T to the edge of the circle along K, T, is, b.

    The area of a circle is .

     is the radius of .

  1. The diameter of is units. is the length of .
    A circle with a center, C, has a tangent line and a secant line which meet outside of the circle. The point of intersection to the point of tangency is 8. The line going from the point of intersection to where the secant line first meets the circle is 4 and the continued distance through the circle is, z, stopping at, B, on the circle. A diameter is drawn from where the secant line first crosses the circle through the center to the opposite side at, A. The distance from A to B is, w.

  1. A hexagon with the following angles going clockwise: 2, x minus 4 degrees, 4, x degrees, x + 8 degrees, 3, x plus 2 degrees, 2, x degrees, x minus 1 degree.

    Refer to the Math Notes box in Lesson 8.1.4 for help calculating the sum of all of the angles in a polygon.

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