11.4 Inscribed Angles. New Vocab: Inscribed Angle and Intercepted Arc.

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Presentation transcript:

11.4 Inscribed Angles

New Vocab: Inscribed Angle and Intercepted Arc

Notice anything cool? 1.Draw a diameter. 2.Put 3 more points anywhere on the circle. 3.Make triangles. What is the measure of all the inscribed angles when they are connected to a diameter? ______

Measure of an Inscribed Angle The measure of an inscribed angle is ____ the measure of its intercepted arc.

Theorem If two inscribed angles of a circle intercept the same arc, then the angles are _____.

Theorem A quad that is inscribed in a circle (called a “cyclic quad”) has opposite angles that are ___________________.

Examples: Find the variable values

Tangent-Chord If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is __________ the measure of its intercepted arc. If <1=60 ⁰, then arc AB=______ (different problem) If arc ACB=256⁰, then <2=_______.

Put it all together…