CIRCLE THEOREMS/POSTULATES SUMMARY

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10 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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CIRCLE THEOREMS/POSTULATES SUMMARY



Draw a diagram for each with appropriate labels. You could be asked to
prove any of the theorems (*’d):


*A radius is perpendicular to a chord (not the diameter) if and only if it bisects
the chord.





*The perpendicu
lar bisector of a chord passes through the center of the circle





*Chords are Congruent if and only if they are equidistant from the center of the
circle.





*Congruent chords cut off congruent arcs (and congruent central angles).





A tangent line is
perpendicular to a radius at the point of tangency. (tautology)





*Two tangent segments drawn to a circle from an external point are congruent.





A central angle = the measure of its intercepted arc





*An inscribed < measures ½ its intercepted arc.




*An angle formed by two chords intersecting inside a circle measures ½ (sum of
intercepted arcs)





*An angle formed by tangents or secants intersecting outside a circle measures
½ (difference of intercepted arcs)





*The sum of the measures of a tange
nt
-
tangent angle and its minor arc is 180






*Opposite angles of a quadrilateral inscribed in a circle are supplementary.





*The product of the segment lengths created by two intersecting chords inside
a circle is constant (ab = cd)





*The product of

the segment lengths created by two intersecting chords outside
a circle is constant (a(a+b)= c(c+d) or a
2

= c(c+d))