Explore angles formed in circles and their relationships. Grade 9 Alberta mathematics.
Lesson 8.3 of Circle Geometry in Grade 9 Math — Alberta curriculum lessons.
In this section, you'll learn what arcs, central angles, and inscribed angles are, and how they relate to each other inside a circle.
An arc is a part of the circumference of a circle — basically, a "slice" of the circle's edge.
There are two types of arcs:.
We usually use the minor arc unless stated otherwise.
A central angle is an angle whose vertex is at the center of the circle.
For example:.
An inscribed angle is an angle formed on the circle itself, not at the center.
Its vertex lies on the circle, and its sides are chords that meet at that vertex.
For example:.
The measure of a central angle is twice the measure of an inscribed angle subtended by the same arc.
In other words:.
"Inscribed angles subtended by the same arc are equal."
That means:. If two or more angles are formed on the circle that open up to the same arc, then those angles will always be equal in measure.
We already know from the previous lesson that:
Central Angle = 2 × Inscribed Angle
In the diagram above:.
In the diagram:.
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