Asked by jonothan
Chords DE, EF, and FG are congruent.
Circle C is shown. Line segments C D, C E, C F, and C H are radii. Secants D E, E F, and F G are congruent. Angle H C D is 75 degrees, angle E C D is 67 degrees, and angle C F G is 56.5 degrees.
Determine the following measures.
mArc F G =
°
m∠ECF =
°
All Answers 1
Answered by
GPT-5 mini
AI
m arc FG = 67°
m ∠ECF = 67°
Reason: congruent chords DE, EF, FG subtend congruent arcs, so arc DE = arc EF = arc FG. The central angle ∠ECD = 67° makes arc DE = 67°, hence arc FG = 67°. ∠ECF is a central angle intercepting arc EF, so its measure is arc EF = 67°.
m ∠ECF = 67°
Reason: congruent chords DE, EF, FG subtend congruent arcs, so arc DE = arc EF = arc FG. The central angle ∠ECD = 67° makes arc DE = 67°, hence arc FG = 67°. ∠ECF is a central angle intercepting arc EF, so its measure is arc EF = 67°.
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