Answer:
Step-by-step explanation:
(A)From the given figure, we have
arc AC=(4x+17)° and ∠ABC=(4x-3.5)°
From the properties of chords in circle, we know
∠ABC=[tex]\frac{1}{2}arcAC[/tex]
⇒[tex]4x-3.5=\frac{1}{2}(4x+17)[/tex]
⇒[tex]8x-7.0=4x+17[/tex]
⇒[tex]4x=24[/tex]
⇒[tex]x=6[/tex]
Therefore, ∠ABC=(4x-3.5)°=4(6)-3.5=24-3.5=20.5° and arcAC=4x+17=4(6)+17=24+17=41°.
(B) It is given that CO is congruent to the segment HZ.
We know that In a circle, if two chords are equal in measure, then their corresponding minor arcs are equal in measure.
Therefore, if CO is congruent to HZ, then arc CO is congruent to arc HZ, hence option D is correct.
