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11-57.

In problem 11-33, you used the relationship between the segment lengths formed by intersecting chords to calculate a missing length. But how are the measures of arcs intercepted by two intersecting chords related? Examine the diagram at right.

2 intersecting chords, divides circle into 4 arcs, labeled as follows: left, 88 degrees, right, c. Angle on left side of intersection, labeled, 72 degrees. Dashed segment, connecting bottom ends of chords, creates triangle, with left bottom angle labeled, b, and right bottom angle labeled, a.

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

    and

    , , and

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

    Find the average of the two arc lengths.