Honors Geometry - Angles Formed by Chords

A chord is a line segment with both endpoints on the circle.

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

The measure of an arc can be calculated using the formula: Arc Measure = (Central Angle / 360) * Circumference of the Circle.

The Inscribed Angle Theorem states that an inscribed angle is half the measure of the intercepted arc.

The angles formed by two intersecting chords can be found using the formula: Angle = (Arc1 + Arc2) / 2.

The measure of the angle formed by a tangent and a chord through the point of contact is equal to half the measure of the intercepted arc.

A secant line is a line that intersects a circle at two points.

The measure of the angle formed by two secants that intersect outside the circle is equal to half the difference of the measures of the intercepted arcs.

The measure of the angle formed by two tangents that intersect outside the circle is equal to half the difference of the measures of the intercepted arcs.

The measure of the inscribed angle that intercepts arc AB is 40°.