MATHEMATICS QUARTER 3

• The set of points in a plane equidistant form a given point(the center of the circle).

  Circle
• Circle:

  • Set of points in a plane equidistant from a given point (the center of the circle)
• Radius:

  • Segment from the center of the circle to a point on the circle (distance from the center to a point on the circle)
• Circumference:

  • Distance around the edge of the circle
• Congruent Circles:

  • Two circles with the same radius
• Diameter:

  • Segment that goes through the center of the circle, with both endpoints on the edge of the circle
• Chord:

  • Line segment that goes from one point to another on the circle's circumference
• Tangent:

  • Line that intersects a circle at only one point
  • Radius at the point of tangency is perpendicular to the tangent line
• Secant:

  • Line that intersects a circle at two points
• Inscribed Angle:

  • Angle made from points sitting on the circle's edge
  • A and C are "end points", B is the "apex point"
• Central angle:

  • Angle with vertex at the center of the circle
• Arc:

  • Part of the circumference (edge) of the circle
  • Measure of an arc is equal to the measure of the central angle formed by its endpoints
  • Arcs are named by their endpoints
• Minor arc:

  • Arc whose measure is less than 180 degrees
• Major arc:

  • Arc whose measure is greater than 180 degrees
• Semicircle arc:

  • Arc whose measure is 180 degrees
• Chord Central Angles Theorem:

  • If two chords in a circle are congruent, they determine two central angles that are congruent
• Chord Arcs Theorem:

  • If two chords in a circle are congruent, their intercepted arcs are congruent
• Perpendicular to a Chord Theorem:

  • Perpendicular from the center of a circle to a chord is the bisector of the chord
• Chord Distance to Center Theorem:

  • Two congruent chords in a circle are equidistant from the center of the circle
• Perpendicular Bisector of a Chord Theorem:

  • Perpendicular bisector of a chord passes through the center of the circle
• Tangent Theorem:

  • A tangent to a circle is perpendicular to the radius drawn to the point of tangency
• Tangent Segments Theorem:

  • Tangent segments to a circle from a point outside the circle are congruent
• Inscribed Angle Theorem:

  • Measure of an angle inscribed in a circle is one-half the measure of the central angle
• Inscribed Angles Intercepting Arcs Theorem:

  • Inscribed angles that intercept the same arc are congruent
• Angles Inscribed in a Semicircle Theorem:

  • Angles inscribed in a semicircle are right angles
• Cyclic Quadrilateral Theorem:

  • Opposite angles of a cyclic quadrilateral are supplementary
• Parallel Lines Intercepted Arcs Theorem:

  • Parallel lines intercept congruent arcs on a circle