Arcs and Angles

Inscribed Angle

The measure of an angle inscribed in a circle is one half the measure of the intercepted arc

Angle COR = arc CRAngle CAR = ½ arc CR or ½ Angle COR

Inscribed Angles Intercepting the Same Arc

Inscribed angles that intercept the same are are congruent

Angle PAQ and Angle PBQ both intercept arc PQ

Angles Inscribed in a Semicircle

If the two chords of the angle have endpoints of the diameter then then angle is 90 degreesOne side of the triangle formed is the diameter

Cyclic Quadrilaterals

A quadrilateral inscribed in a circleAll the vertices of the quad touch the circleThe opposite angles of a cyclic quadrilateral are supplementary

Examples

Homework

Pg 327 1-13 oddHonors 16 and 17