Circle Theorems

• Central angle theorem

  • the measure of the central angle is equal to the measure of the intercepted arc

  
• Inscribed Angles Theorem

  • the measure of an inscribed angle is half the measure of the intercepted arc

  
• Inscribed Angles Theorem

  • an angle inscribed in a semicircle must be a right angle

  
• Inscribed Angles Theorem

  • inscribed angles that intercept the same arc are congruent

  
• Inscribed Angles Theorem

  • inscribed angles that intercept congruent arcs are congruent

  
• Inscribed Angles Theorem

  • parallel chords intercept congruent arcs

  
• Congruent chords intercept congruent arcs

  
• congruent chords are equidistant to the center of the circle

  
• A perpendicular bisector of a chord must go through the center of the circle

  
• tangent radius theorem

  • a tangent line and a radius are perpendicular

  
• tangents from the same external point theorem

  • tangent segments from the same external points are congruent

  
• an angle formed by a chord and a tangent line at the point of tangency is half the measure of the intercepted arc

  
• Chord Chord Theorem

  • the measure of an angle formed by two lines that intersect inside a circle is the average of the measure of the intercepted arcs

  
• secant secant theorem

  • the measure of an angle formed by two lines that intersect outside the circle is half the difference between the intercepted arcs

  
• tangent secant theorem

  • the measure of an angle formed by two lines that intersect outside a circle is half the difference between the intercepted arcs.

  
• chord segments theorem

  • if two chords intersect, the product of the measures of the segment of one chord is equal to the product of the measures of the segments of the other

  
• secant segments theorems

  • if two secant segments are drawn to a circle from an external point, then the product of the lengths of one secant segment and its external segment is equal to the product of the lengths of the other secant segment and its external segment

  
• tangent secant segments

  • if a tangent and a secant are drawn to a circle from an external point, then the square of the length of the tangent segment is equal to the product of the length of the secant segment and its external segment