AMSCO'S Geometry. New York - Rye High School

596 Geometry of the CircleFormulas(Continued)Type of Angle Degree Measure ExampleFormed by aTangent and aChordFormed by TwoIntersectingChordsThe measure of an angleformed by a tangent and achord that intersect at thepoint of tangency is equal toone-half the measure of theintercepted arc.The measure of an angleformed by two intersectingchords is equal to one-halfthe sum of the measures ofthe arcs intercepted by theangle and its vertical angle.A1Bm/1 5 1 X2 mABDC2 1m/1 5 1 2 (mABm/2 5 1 2 (mABABX 1 mCD X )X 1 mCD X )Formed byTangents andSecantsThe measure of an angleformed by a tangent and asecant, two secants, or twotangents intersecting outsidethe circle is equal toone-half the difference ofthe measures of theintercepted arcs.ABCC1 2C DABA3Bm/1 5 1 2 (mAB X 2 mAC X )X 2 mCD X )m/2 5 1 2 (mABm/3 5 X 1 2 (mACB 2 mAB X )