Given: k(o, r), ab = bc
m∠b =120°, r=14cm
find: ab

AB=14 cm

Step-by-step 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

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: