A minor arc is an arc that measures less than 180^(∘). A major arc is an arc that measures greater than 180^(∘).
A semicircle is an arc with endpoints that lie on a diameter.
Type: Minor arc Measure: 43 ^(∘)
Practice makes perfect
An arc is a portion of a circle defined by two endpoints. A central angle separates the circle into two arcs — the major arc and the minor arc. These measures of these arcs are related to the measure of the central angle.
Arc
Measure
A minor arc is the shortest arc connecting two endpoints on a circle.
The measure is less than 180^(∘) and is equal to the measure of its related central angle.
A major arc is the longest arc connecting two endpoints on a circle.
The measure is greater than 180^(∘) and is equal to 360^(∘) minus the measure of the minor arc with the same endpoints.
Now, let's consider the given diagram. Note that ABD has endpoints that lie on a diameter. This means that ABD is a semicircle and therefore mABD=180^(∘).
The arc that we are looking at is BC. It is the shortest arc that connects the endpoints B and C. Therefore, BC is a minor arc. To find its measure, we will need to use the Arc Addition Postulate. With this postulate and knowing that mABD=180^(∘), mAB=67^(∘) and mCD=70^(∘), we can find mBC.
