Geo Chap. 10.1-7 Theorems

If a radius is perpendicular to a chord…

It bisects the chord

If a radius of a circle bisects a chord that is not the diameter…

Then it is perpendicular to the chord

A perpendicular bisector of a chord pass through…

The center of the circle

If two chords of a circle are equidistant from the center…

Then they are congruent

If two chords of a circle are congruent…

Then they are equidistant from the center of the circle

If two central angles of a circle (or of congruent circles) are congruent…

Then their intercepted arcs are also congruent

If two arcs of a circle (or of congruent circles) are congruent…

Then their corresponding central angles are congruent

If two central angles of a circle (or of congruent circles) are congruent…

Then their corresponding chords are congruent

If two chords of a circle (or of congruent circles) are congruent…

Then their corresponding central angles are congruent

If two arcs of a circle (or of congruent circles) are congruent…

Then their corresponding chords are congruent

If two chords of a circle (or of congruent circles) are congruent…

Then their corresponding arcs are congruent

If two tangent segments are drawn to a circle from an external point…

Then those segments are congruent

The measure of an inscribed angle or a tangent-chord angle (vertex on a circle) is…

½ the measure of it’s intercepted arc

The measure of a chord-chord angle is…

½ the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle

The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside a circle) is…

½ the difference of the measures of the intercepted arcs

If two inscribed or tangent-chord angles intercept the same arc…

Then they are congruent

If two inscribed or tangent-chord angles intercept congruent arcs…

Then they are congruent

An angle inscribed in a semicircle is…

A right angle

The sum of the measures of a tangent-tangent angle and its minor arc is…

180

If a quadrilateral is inscribed in a circle, it’s opposite angles are…

Supplementary

If a parallelogram is inscribed in a circle, it must be a…

Rectangle