Chapter 12 Postulates & Theorems

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Standard Equation of a Circle

The standard equation of a circle with center (h,k) and radius r is (x-h)²+(y-k)²=r²

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs

In a plane, a line is tangent to a circle IFF

the line is perpendicular to a radius of the circle at its endpoint on the circle

congruent

In the same circle, or in congruent circles, two minor arcs are congruent IFF

their corresponding chords are congruent

If one chord is the perpendicular bisector of another chord

then the first chord is a diameter

If a diameter of a circle is perpendicular to chord,

then the diameter bisects the chord and its arc

In the same circle, or in congruent circles, two chords are congruent IFF

they are equidistant from the center

Measure of an Inscribed Angle Theorem

The measure of an inscribed angle is one half the measure of its intercepted arc

If two inscribed angles of a circle intercept the same arc,

then the angles are congruent

An angle inscribed in a semicircle

is a right angle.

supplementary

If a tangent and a chord intersect at a point on a circle,

then the measure of each angle formed is one half the measure of its intercepted arc

Example:

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