Circles: Special Angles and Arcs in Circles

Arcs of Circles

In this section we are studying angles and arcs in circles. Let's start by defining different types of arcs and how they are related.

Arcs fall in three categories: minor arcs, major arcs and semi-circles.

Minor arcs are the shortest distance along a circle connecting two points.  Minor arcs measure less than 180°.  Major arcs are the longest distance along a circle connecting two points. Major arcs measure greater than 180°.


Take a look the circle below.

Circle with minor arc AB highlighted in red and major arc ACB highlighted in blue
Circle with minor arc AB and major arc ACB


There are two arcs with endpoints A and B.  The first is minor arc AB, marked in red.  The second is major arc ACB, marked in blue.  Notice that when we name the major arc, we use a third point on the circle to indicate that the arc passes through that point.

An arc with measure exactly 180° is called a semi-circle.


Circle P with diameter XZ and point Y on the circle
Circle P

XZ is a diameter, so arc XYZ measures 180°. arc XYZ is a semi-circle.