Answer:
AB=14 cm
Explanation:
step 1
Find the measure of major arc AC
we know that
The inscribed angle is half that of the arc it comprises.
so
m∠B=(1/2)[major arc AC]
we have
m∠B=120°
substitute
120°=(1/2)[major arc AC]
240°=major arc AC
so
major arc AC=240°
step 2
Find the measure of arc ABC
we know that
arc AC+arc ABC=360°
substitute
240°+arc ABC=360°
arc ABC=120°
step 3
Find the measure of angle AOC
m∠AOC=arc ABC=120° ------> by central angle
so
The triangle AOC is an isosceles triangle
OA=OC=14 cm ------> is the radius
The internal angles of triangle AOC are
m∠CAO=m∠OCA=30°
The triangle ABC is an isosceles triangle
AB=BC
The internal angles of triangle ABC are
m∠BAC=m∠ACB=30°
so
Triangles AOC and ABC are congruent by ASA similarity postulate ( two angles and included side)
therefore
AO=AB=14 cm