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Home > CCG > Chapter 11 > Lesson 11.2.3 > Problem 11-111

11-111.

In part (c) of problem 11‑110, you used the relationship between the segment lengths formed by intersecting chords to find a missing length. But how are the arc measures of two random intersecting chords related? Examine the diagram at right.  

  1. Solve for , and  using what you know about inscribed angles and the sum of the angles of a triangle.

    Look above at the image of the circle.
    because they are supplementary angles.

    Use the Triangle Angle Sum Theorem to solve for .

  1. Compare the result for with  and . Is there a relationship?

    Since c is equal to , the vertical angles () are the average of the two arcs they intercept.