CPM Homework Help : INT2 Problem 10-66

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10-66.

In $⊙A$ at right, $m∠C = 64°$ . What is:

$m∠D$ ?
Hint (a):
How do the end points of $∠C$ and $∠D$ relate?

$m\overarc { B F }$ ?
Hint (b):
Notice $ΔCBA$ . If A is the center, then what is true about the lines $AC$ and $AB$ , and consequently $∠C$ and $∠B$ ?
More Help (b):
What is true about the sum of $m∠CAB$ and $m∠BAF$ ?
Answer (b):
$128°$

$m∠E$ ?
Hint (c):
See hint from part (a).

$m\overarc { C B F }$ ?
Hint (d):
If A is the center, then the line $CF$ must be the circle's diameter.
What does that mean for the the arc or semi-circle?
Answer (d):
$180°$

$m∠BAF$ ?
Hint (e):
See hints for part (b).

$m∠BAC$ ?
Hint (f):
Use the answer from part (e) and hints from part (b).
Answer (f):
$52°$

A circle, with center point A, has 5 points clockwise about the circle, B, F, E, D, C, Line segments connect the following pairs of points: from, C to F, through, A, from, A, to B, from, B, to C, from, B, to D, from, B, to E, from, D to F, from, F to e.