Points A and B are marked on the circle centered at point O so that ∠AOB = 20 °.

Points A and B are marked on the circle centered at point O so that ∠AOB = 20 °. The length of the smaller arc AB is 88. Find the length of the larger arc AB.

Given:

a circle centered at point O;

∠AOB = 20 °;

smaller arc AB = 88 cm.

Find: the length of the greater arc AB -?

Decision:

∠AOB is the central, and the central angle is equal to the arc on which it rests, hence the smaller arc AB = 20 °.

Since the degree measure of the entire circle is 360 °, therefore the large arc AB = 360 ° – 20 ° = 340 °.

Let’s solve the problem using proportion.

Take the large arc AB as x cm.

We get:

20 ° – 88,

340 ° – x.

Let’s make the proportion:

20: 340 = 88: x,

x = (340 * 88) / 20,

x = 1496 (cm) – the length of the larger arc AB.

Answer: 1496.