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# Geometry Chapter 12 Notes

The radius is perpendicular to the point of tangency (the place where the line touches the circle) of a tangent line

If a line touches a circle only once then it is tangent

2 tangent lines that have 1 one the same endpoint are congruent

In circles, congruent central angles have congruent chords (Thm)

In circles, congruent chords have congruent central angles (Converse)

In circles, congruent central angles have congruent arcs (Thm)

In circles, congruent arcs have congruent central angles (Converse)

In circles, congruent chords have congruent arcs (Thm)

In circles, congruent arcs have congruent chords (Converse)

If 2 chords are equidistant from the center of a circle, then they are congruent (Thm)

If 2 chords are congruent, then they are equidistant from the center of a circle (Converse)

If the diameter line of a circle is perpendicular to a chord, then it will split the chord (that is not a diameter itself) and the arc in half (Thm)

The perpendicular bisector of a chord contains the center of a circle (Thm)

Inscribed angles are angles that are only in a circle (Definition)

Circumscribed angles are angles that are not inside a circle (Definition)

Inscribed Angle Theorem: The measure of a inscribed angle is half the measure of its intercepted arc (Thm)

Corollaries to Inscribed Angle Theorem:

Corollary 1: 2 inscribed angles with the same intercepted arcs are congruent

Corollary 2: A semicircles inscribed angle is a right angle

Corollary 3: Quadrilaterals inscribed in circle opposite angles are supplementary

The measure of the angle formed by tangent line and a chord is 1/2 of the intercepted arc (The measure of the inscribed angle and the measure of the angle formed by the tangent line and chord is the same) (Thm)

Secant is a line that intersects a circle twice (Definition)

Measure of angle formed by 2 secants is half the measures of the 2 intercepted arcs (Thm)

Measure of angle that intersects outside of circle is half the difference between the 2 arcs (Thm)

In a circle, if you place a point, and draw a line, then the 2 segments (each side of the point) will have the same product no matter what (Thm)

The equation of a circle is (with center of h, k) (x-h)squared + (y-k)squared = r(squared)

A locus is a set of points that meet a condition (Definition)

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