Finding Inscribed Angle Measurements

~Inscribed Angle is an angle whose vertex lies on a circle and whose sides are chords of the circle
~Inscribed Angle Theorem is the the
measure of an angle inscribed in a circle is equal to 1/2 the measure of the intercepted arc

M<ABC = 1/2mAC(the intercepted ark of AC)

external image inscribed_angle_abc.jpg


external image inscribed-angle-error.gifmeasue of angle X is 90 drgrees because 1/2 of the ark
  • If YZ is a diameter of circle
  • and <YZX is an inscribed angle
  • then<YZX is a right angle
  • Right Angle Corollary is if an inscribed angle intercepts a semicircle, then the angle is a right angle

Finding Central Angle Measurements

A central angle is an angle whose vertex is the center of circle and the sides pass through a pair of points on the circle
external image 320px-Sector_central_angle_arc.svg.pngexternal image circle1.gifx = 80 degrees
  • measue of a central angle is equal to the measure of the minor ark
  • Central Angle

external image CentralInscribedAngle_700.gif

    • inscribed angle is half of the central angle with common endpoints
    • so then a central angle is double the measure of a inscribed angle with common endpoints