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The Circle and Some Related Terms

  • Circle–The set of all points in a plane at a given distance from a given point.

    • The set of all point equidistant from a given point called the center of the circle.

    • The given point is the center of the circle and the given distance is the radius.

  • Radius–It is defined as a segment connecting the center with a point on the circle. (radii –plural)

  • Chord–A segment whose endpoints lie on the circle.

  • Diameter–A chord that contains the center of the circle.

    • Not all chords can be a diameter.

    • It divides a circle into two congruent arcs called semicircles

  • Arc–A portion of a circle where two distinct points on a circle divides the circle into two parts.

    • Two distinct points on a circle divide the circle into parts called arcs.

  • 3 Classifications of Arcs

    • Minor Arc–Less than 180 degrees

    • Major Arc–Greater than 180 degrees

    • Semicircle–Exactly 180 degrees

  • Tangent Line–A tangent to a circle is a line, coplanar with the circle that intersects the circle in exactly one point.

  • Secant Line–A secant line is a line that intersects the circle in two points. It is always composed of a chord.

  • Exterior of the circle–It is a set of points in the plane of the circle whose distance from the center is greater than the radius.

    • The circle is divided into 3 parts: Exterior, Interior and the circle itself

  • Central Angle–It is an angle in the plane of the circle whose vertex is the center of the circle.

  • Inscribed Angle–An angle whose vertex lies on the circles and whose sides contain points of the circle.

  • Inscribed Polygon–It is a polygon whose sides are chords of a circle. The polygon is inscribed in a circle, and the circle is circumscribed about the polygon.

  • Circumscribed Polygon–The polygon is outside the circle.

  • Common Tangent –It is a tangent to each of coplanar lines.

  • Common External Tangent–The line did not intersect the center of the circle

  • Concentric Circles–Two or more circles with the same center.

  • Congruent Circles–The circles have the same radius.

D

The Circle and Some Related Terms

  • Circle–The set of all points in a plane at a given distance from a given point.

    • The set of all point equidistant from a given point called the center of the circle.

    • The given point is the center of the circle and the given distance is the radius.

  • Radius–It is defined as a segment connecting the center with a point on the circle. (radii –plural)

  • Chord–A segment whose endpoints lie on the circle.

  • Diameter–A chord that contains the center of the circle.

    • Not all chords can be a diameter.

    • It divides a circle into two congruent arcs called semicircles

  • Arc–A portion of a circle where two distinct points on a circle divides the circle into two parts.

    • Two distinct points on a circle divide the circle into parts called arcs.

  • 3 Classifications of Arcs

    • Minor Arc–Less than 180 degrees

    • Major Arc–Greater than 180 degrees

    • Semicircle–Exactly 180 degrees

  • Tangent Line–A tangent to a circle is a line, coplanar with the circle that intersects the circle in exactly one point.

  • Secant Line–A secant line is a line that intersects the circle in two points. It is always composed of a chord.

  • Exterior of the circle–It is a set of points in the plane of the circle whose distance from the center is greater than the radius.

    • The circle is divided into 3 parts: Exterior, Interior and the circle itself

  • Central Angle–It is an angle in the plane of the circle whose vertex is the center of the circle.

  • Inscribed Angle–An angle whose vertex lies on the circles and whose sides contain points of the circle.

  • Inscribed Polygon–It is a polygon whose sides are chords of a circle. The polygon is inscribed in a circle, and the circle is circumscribed about the polygon.

  • Circumscribed Polygon–The polygon is outside the circle.

  • Common Tangent –It is a tangent to each of coplanar lines.

  • Common External Tangent–The line did not intersect the center of the circle

  • Concentric Circles–Two or more circles with the same center.

  • Congruent Circles–The circles have the same radius.