Question

Find the arc that is congruent to arc BF.

Answer 1

Answer: choice 2) arc CDE

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There's a lot going on in this diagram. It might help to use a highlighter or a different pen to mark only what we care about. I marked arc BF in red. The corresponding central angle that goes with arc BF is marked in blue. This is angle BAF. Point A is the center of the circle, so angle BAF is a central angle. We don't know the measure of angle BAF, but we know that it is congruent to angle CAE (marked in green). Why? Because they are vertical angles. Vertical angles are always congruent.

Angle CAE is the central angle that cuts off arc CDE (marked in purple), so we can form this chain of equations:

arc BF = angle BAF
angle BAF = angle CAE
angle CAE = arc CDE

which in short shows
arc BF = arc CDE

note: when I say "arc BF", I mean "minor arc BF" which is the shortest route from B to F. So we go from B to F without going through any other point on the circle.