Geometry: Geometry of Circles

Angles and Arcs of Circles

The first topic that we need to discuss is angles and arcs of circles. Arcs and angles in circles are connected, and we can discuss both at the same time. Arcs are placed into three distinct categories, minor arcs, major arcs, and a semicircle. Let’s take a closer look at the properties of these arcs and how they relate to angles.

A minor arc is the shortest arc connecting two endpoints on a circle. The following is a circle with a center at point L. A circle is denoted by the symbol "circle L".

Circle L with points K, H, N on the circle and central angle HLN

Arc HN is called the minor arc. It is denoted by the symbol "arc H N". angle H L N is called the central angle. We know that the measure of arc HN equals the measure of angle HLN.

A major arc is the longest arc connecting two endpoints on a circle.

Circle L with points K, H, N on the circle and central angle HLN

Arc HKN is the major arc of circle L. Therefore measure of arc HKN equals 360 minus the measure of arc HN. Remember that a circle has measures 360° all the way around. If we take the measure of the entire circle and subtract the minor arc, we will be left with the major arc.

Finally, a semicircle is an arc with endpoints that line on a diameter. The measure of a semicircle is 180° since it is half of the circle.

Circle B with diameter AC and point D on the circle

the measure of arc ADC equals 180 degrees since it is a semicircle.