9. ; ;
; ; ;
- meters
InscribedAngles
LearningObjective
- Find the measureof inscribedanglesand the arcs they intercept
InscribedAngle,InterceptedArc
Aninscribedangleis an anglewhosevertexis on the circleand whosesidescontainchordsof the circle.
An inscribedangleis said tointerceptan arc of the circle.We will proveshortlythat the measureof an in-
scribedangleis half of the measureof the arc it intercepts.
Noticethat the vertexof the inscribedanglecan be anywhereon the circumferenceof the circle--itdoesnot
needto be diametricallyoppositethe interceptedarc.
Measureof InscribedAngle
The measureof a centralangleis twicethe measureof the inscribedanglethat interceptsthe samearc.
Proof.