Answer:
Arc BC = arc DC because their subtended chords BC and DC are equal
Step-by-step explanation:
∵ CE is a diameter of circle A(chord passing through the center of the circle)
∵ CE ⊥ to the chord BD and intersect it at F
∴ BF = FD ⇒ fact in the circle
In the 2 Δ CFB and CFD
∵ BF = DF
∵ m∠BFC = m∠DFC = 90°
∵ CF is a common side
∴ The two triangles are congruent
∴ BC = DC
In the circle if the two chords are equal in lengths then their subtended arcs are equal in lengths and measures
∴ Arc BC = arc DC
