# 6.3 – Arcs

Key Terms

• Arc – A part of the circumference of a circle.
• The symbol $\widehat{AB}$ means “the arc with endpoints A and B.”
• Central Angle – An angle that has its vertex at the center of the circle.
• Major Arc – An arc of a circle that is longer than half the circumference.
• The degree measure of a major arc is greater than 180°
• Minor Arc – An arc of a circle that is shorter than half the circumference.
• The degree measure of a minor arc is less than 180°.
• Semicircle – A 180° arc; half of a circle.

Review

• Play the circle review game on Pg 1 in Apex Study 6.3

Notes

• Arcs
• Like a line segment, an arc has a point at each end, called an endpoint.

• Central Angles
• An angle whose vertex is at the center of a circle.
• The sides of a central angle are two radii of the circle.
• The sides of a central angle (the radii) intercept the circle and form an arc.
• To intercept means “to intersect,” “to stop the course of,” or “to mark off.”
• It stops the course of the arc around the circumference of the circle.
• It marks off the length of the arc

• Minor Arc
• An arc that lies between the two sides of a central angle that measures less than 180°.
• Notation: $\widehat{AB}$  <– The arc above AB should look more curvy (like the one below)

• Major Arc
• A major arc lies outside of the central angle that is created by a minor arc, and it measures more than 180°.
• The middle point in a major arc name is a point on the arc between its two endpoints.
• Notation: $\widehat{AXB}$  <– The arc above AXB should look more curvy (like the one below)

• Semicircle
• An arc that measures 180° created by the diameter’s endpoints.

Examples

• Ex 1. Given $\odot{O}$ below, $\widehat{XY}$ is a minor arc, a major arc, or a semicircle?
• Because it is less than 180°, it is a minor arc.

• Ex 2. What is the measure of $\widehat{ACB}$ in $\odot{O}$ below?
• Since circles have a total degree measure of 360°, you must subtract the minor arc (given: 30°) from 360° to find the major arc.