Math Theorems Maam Korina

• Theorem 1: If two central angles of a circle have equal measures,then their correponding minor arcs have equal measures
• Theorem 2:In a circle,if two minor arcs are equal in measure, then their corresponding chords are congruent
• Theorem 3:Two chords of congruent circles are congruent if only if they subtend congruent arcs
• Theorem 4 :If a radius is perpendicular to a chord,then it bisects the chord
• Theorem 5: If a radius bisects a chord then its perpendicular to the chord
• Theorem 6: In a circle,if two chords have the same distance from the center then the chords are congruent.
• Theorem 7 :In a circle if two chords are congruent, then they have the same distance from the center
• Theorem 8:The measure of an inscribed angle intercepting an arc of a circle is half of the measure of the central angle intercepting the same arc.

  Corollary 1: Inscribed angle intercepting the same arc are congruent

  Corollary 2:If an inscribed angles intercepts the circle at the endpoints of a diameter ,then the inscribed angle is a right angle
• Theorem 9:If two parallel lines intersect a circle then the intercepted arcs between the lines are congruent
• Theorem 10 :The opposite interior angles of a cyclic quadrilateral are supplementary angles.
• is a line,segment ,or ray ,that intersects the circle at exactly one point

  Tangent
• If a line is tangent then its perpendicular to the radius at the point of tangency.


  Theorem 11
• Corollary 1: Two tangents with one endpoints on the circle and the other endpoint a common external point have the same length.
• Corollary 2: two tangents with one endpoint on the circle and the other endpoint a common external point form an angle that is bisected by the segment connecting the external point and the center of the circle
• Theorem 12: If a line is perpendicular to a radius of a circle and intersects that intersects that radius at its endpoints on the circle then it is tangent to the circle.
• A secant of a circle is line segment,or ray that intersects the circle at exactly two points.


  secants