Circles.

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Presentation transcript:

Circles

10.3-10.4

Congruent Corresponding Chords Theorem In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Perpendicular Chord Bisector Theorem & Converse The diameter of a circle is perpendicular to a chord iff the diameter bisects the chord and its arc.

What is the measure of Arc CD in the figure below?

Equidistant Chords Theorem In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center.

What is the value of x for the circle below?

Intercepted Arc An inscribed angle is an angle whose vertex is on a circle. An Intercepted arc is the arc in the interior of the angle.

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

Inscribed Polygon A polygon is an inscribed polygon if all of its vertices lie on a circle. The circle that contains the vertices is circumscribed circle.

Theorem A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

Practice P.553: 3-10, 15 P.562: 3-16