For AI agents: use /llms.txt for the Nakafa content index.
A central angle is an angle formed by two radii of a circle with the vertex located at the center of the circle. The sides of the central angle are radii that connect the center to points on the circle.
In the figure above:
An inscribed angle is an angle formed by two chords with the vertex located on the circle. The sides of the inscribed angle are chords that connect the vertex to two other points on the circle.
In the figure above:
Central angles and inscribed angles that subtend the same arc have a special relationship. Let's observe this relationship.
If a central angle and an inscribed angle subtend the same arc, then:
Let's prove the relationship between central angle and inscribed angle by constructing auxiliary lines.
Proof steps:
Inscribed Angle Subtending a Diameter
Every inscribed angle that subtends a diameter of a circle measures (right angle).
Inscribed Angles Subtending the Same Arc
, both angles subtend the same arc .
Given central angle . Find the measure of inscribed angle that subtends the same arc!
Solution:
Given inscribed angle . Find the measure of central angle that subtends the same arc!
Solution:
If the central angle of a circle is , what is the measure of the inscribed angle that subtends the same arc?
Inscribed angle . Find the measure of central angle !
In a circle, inscribed angle subtends a diameter. What is the measure of angle ?
Two inscribed angles subtend the same arc. If one angle measures , find the measure of the other angle!
Inscribed angle is
Central angle
(an inscribed angle subtending a diameter is always )
The other angle is (inscribed angles subtending the same arc have equal measures)
