Chapter 11 Postulates and Theorems
If a line is tangent to a cirlce, then it is perpendicular to the radius drawn to the point of tangency
Converse Tangent-Radius Theorem-w
If a line is perpendicular to the radius, then the line is tangent to the circle
External Point-Tangent Theorem-w
If two segments are tangent to a circle from the same external point, then the segments are congruent.
Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs
Central Angle, Chords, and Arcs Theorem-w
In a circle or congruent cirlces:
1. Congreunt central angles have congruent chords
2. Congruent chords have congruent arcs
3. Congruent arcs have congruen central angles.
Perpendicular Radius Theroem-w
In a cirlce, if a radius (or diameter) is perpendicular to a chord, then it bsects the chrd and its arc
Perpendicular Chord Bisector-w
In a circle, the perpendicular bisector of a chord is a radius (or diameter).
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
Inscribed Angle Corrolary-w
If inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc, then the angles are congruent.
Inscribed Angle Subtending Theorem-w
an inscribed angle subtends a semicircle if and only if the angle is a right angle.
Inscribed Quadrilateral Theorem-w
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
Tangent/Secant Intersection Theorem-w
If a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measur off the intercepted arc
Secand/Chord Intersection Theorem-w
If two secants or chords intersect on the interior of a circle then the measure of each angle formed is half the sum of the measure of the sum of the two measures
Tangent/Secant Exterior Intersection Theorem-w
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of tthe intercepted arc