Angle Relationships (Vertex On, Inside & Outside) Name Theorem Hypothesis Conclusion If a tangent and a chord intersect at a point on the circle, then Tangent Chord Theorem the measure of each (Vertex On) angle formed is one half the measure of its intercepted arc. Example: Find the measure of 1. Example: Find the measure of arc EFG. Name Theorem Hypothesis Conclusion If two chords intersect inside the circle, then the measure of each Interior Angles of a Circle angle is half the sum of Theorem the measures of the arcs (Vertex Inside) intercepted by the angle and its vertical angle. Example: Find x and y. Example: Find the value of x. Name Theorem Hypothesis Conclusion If a tangent and a secant, two tangents, or two secants intersect Exterior Angles of a outside the circle, then Circle Theorem the measure of the (Vertex Outside) angle formed is half the difference of the measures of the intercepted arcs. Find the value of x. Find the value of x. Example: Example:
Angle Relationships (Vertex On, Inside & Outside) Name Theorem Hypothesis Conclusion Tangent Chord Theorem (Vertex On) If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed is one half the measure of its intercepted arc. Example: Find the measure of 1. Example: Find the measure of arc EFG. Name Theorem Hypothesis Conclusion Interior Angles of a Circle Theorem (Vertex Inside) If two chords intersect inside the circle, then the measure of each angle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Example: Find x and y. Example: Find the value of x. Name Theorem Hypothesis Conclusion Exterior Angles of a Circle Theorem (Vertex Outside) If a tangent and a secant, two tangents, or two secants intersect outside the circle, then the measure of the angle formed is half the difference of the measures of the intercepted arcs. Example: Find the value of x. Example: Find the value of x.
Day-1-Notes-Parts-of-Circles-on-level-2mpm1s3.docx