Secants, Tangents, and Angle Measure

Intersections On or Inside a Circle that intersects a circle A line that intersects a circle in exactly two points is called a secant

Intersections On or Inside a Circle If two secants or chords intersect in the interior of a circle then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle

Intersections On or Inside a Circle is one half the sum of the measure by the angle and its vertical angle then the measure of the angle formed intersect in the interior of a circle If two secants or chords of the arcs intercepted x 1 y

Intersections On or Inside a Circle 45 65 1

Intersections On or Inside a Circle If a secant (or chord) and a tangent intersect at the point of tangency Then the measure of each angle formed is one half the measure of its intercepted arc.

Intersections On or Inside a Circle of its intercepted arc Then the measure of each angle formed is one half the measure If a secant (or chord) and a tangent intersect at the point of tangency x y 1 2

Intersections On or Inside a Circle 200 160 1 2

Intersections Outside a Circle If secants and tangents intersect outside a circle they form an angle whose measure is related to the intercepted arcs

Intersections Outside a Circle If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle then the measure of the angle formed is one half the difference of the measures of the intercepted arcs

Intersections Outside a Circle Two secants 1 y x

Intersections Outside a Circle A secant and a tangent x y 1

Intersections Outside a Circle Two tangents x y 1