# CIRCLE THEOREMS/POSTULATES SUMMARY

Ηλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 4 χρόνια και 7 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))