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This guide provides an overview of essential circle geometry concepts, including definitions and key theorems. You'll learn about important terms such as radius, diameter, secant, tangent, and chord, along with types of angles like inscribed and central angles. Key theorems related to congruency and relationships between angles and arcs are also discussed. This resource is perfect for students looking to deepen their understanding of circle geometry concepts, essential for solving mathematical problems involving circles.
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Allie Buksha 6-9-09 Geometry Mr. Chester Circle Proofs
VOCABULARY • RADIUS- a line segment drawn from the center point to a point on the circle • DIAMETER – a line segment from one point on the circle to another, and passes the center point • SECANT – a line segment drawn from an external point to a point on the circle while passing through the circle once. • TANGENT– a line segment drawn from an external point to a point on the circle, and it extended wont intersect the circle again • CHORD – a line from one point on the circle to another
TYPES OF ANGLES • INSCRIBED ANGLES – an angle formed by two chords with the vertex on the circle • CENTRAL ANGLES – an angle formed by two radii with the vertex on the circle
THEOREOMS • All radii of a circle are congruent • In a circle, congruent central angles have congruent arcs • In a circle, congruent arcs have congruent chords and vice versa • A diameter perpendicular to a chord bisect the chord and its arcs • Congruent chords in the same circle are equidistant from the center of the circle • In a circle, if two chords are unequal, the shorter chord is farther from the center • An angle inscribed in a semicircle is a right angle • In a circle, inscribed angles that intercept the same arc are congruent • Parallel lines intercept congruent arcs • If a line is tangent to a circle then it is perpendicular to the radius at that point • Two tangent segments drawn to a circle from an external point are congruent
