10.5 Notes Date: _____________________
Angles with Vertices on a Circle
Definition An inscribed angle is an angle whose vertex is on a circle and whose sides are
determined by two chords.
Definition A tangent-chord angle is an angle whose vertex is on a circle and whose sides are
determined by a tangent and a chord that intersect and the tangent’s point of contact.
Theorem The measure of an inscribed angle or a tangent-chord angle (vertex on a circle) is one-half the measure of
its intercepted arc.
Angles with Vertices Inside, But Not at the Center of a Circle
Definition A chord-chord angle is an angle formed by two chords that intersect inside a circle, but not at the center.
Theorem The measure of a chord-chord angle is one-half the sum of the measures of the arcs intercepted by the
chord-chord angle and its vertical angles.
