
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.
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
.
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.