Part 1: Tangent-Chord Angles

Angle JCB is a tangent-chord angle with vertex C.

The vertex of a tangent-chord angle is:

outside the circle inside the circle at the center of the circle on the circle

Tangent-Chord Angles

Notice that [math]\angle CAB[/math] and [math]\angle JCB[/math] share a common intercepted arc. What is the relationship between a tangent-chord angle and its intercepted arc?

[math]\text{m\angle{JCB} = m\overset{\frown}{CB}}[/math] [math]\text{m\angle{JCB} + m\overset{\frown}{CB} = 180}[/math] [math]\text{m\angle{JCB} = 2m\overset{\frown}{CB}}[/math] [math]\text{m\angle{JCB}=\frac{1}{2}m\overset{\frown}{CB}}[/math]

How is a tangent-chord angle similar to an inscribed angle?

Information: Part 1: Tangent-Chord Angles