MATH

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Created by
Jameer Go

Cards (15)

  • Theorem 1
    If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.
  • Theorem #2 - If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.
  • Corollary #1 - Two tangent segments from a common external point are congruent.
  • Corollary #2 - The two tangent rays from a common external point determine an angle that is bisected by the ray from the external point to the center of the circle.
  • Theorem #3 - If in a circle a radius bisects a chord, then the radius is perpendicular to the chord.
  • Theorem #4 - If in a circle a radius is perpendicular to a chord, then the radius bisects the chord.
  • Theorem #5 - The Arc Addition Theorem
    The measure of an arc formed by two adjacent nonoverlapping arcs (arcs that share exactly one point) is equal to the sum of the measures of these two arcs.
  • Theorem 6 - The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.
  • Corollary 3 - An angle inscribed in a semicircle is a right angle.
  • Corollary 4 - Angles inscribed in the same arc are congruent.
  • Corollary 5 - The opposite angles of an inscribed quadrilateral are supplementary.
  • Theorem 7 - The Tangent-Secant Theorem
    Given an angle with its vertex on a circle, formed by a secant ray and a tangent ray, the measure of the angle is one-half the measure of the intercepted arc.
  • Theorem 8 - If two chords intersect within a circle, then the measure of the angle formed is equal to one half the sum of the measures of the intercepted arcs.
  • Theorem 9 - If a tangent and a secant, two secants, or two tangents intersect in a point in the exterior of a circle, then the measure of the angle formed is equal to one-half the difference of the measures of the intercepted arcs.
  • Theorem 10 - If two chords intersect inside a circle, then the product of the lengths of the segment parts of one chord is equal to the product of the lengths of the segment parts of the other chord.