CPM Homework Help : CCG Problem 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 $a$ , $b$ , and $c$ using what you know about inscribed angles and the sum of the angles of a triangle.
Hint (a):
$88º = 2a$
More Help (a):
Look above at the image of the circle.
$72º + d = 180º$ because they are supplementary angles.
Hint 2(a):
Use the Triangle Angle Sum Theorem to solve for $b$ .
$c = (2)(∠b)$

Compare the result for $c$ with $88º$ and $72º$ . Is there a relationship?
Answer (b):
Since c is equal to $56º$ , the vertical angles ( $72º$ ) are the average of the two arcs they intercept.
$\frac{88 + 56}{2} = 72º$