Geometry: 12-1 - 12-3 Theorems

Theorem 12-6

- in a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs

Theorem 12-8

- in a circle, the perpendicular bisector of a chord contains the center of a circle

Theorem 12-10

- the measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc

Theorem 12-9

- the measure of an inscribed angle is half the measure of its intercepted arc

Theorem 12-3

- the two segments tangent to a circle from a point outside the circle are congruent

Corollaries to the Inscribed Angle Theorem

- two inscribed angles that intercept the same arc are congruent - an angle inscribed in a semicircle is a right angle - the opposite angles of a quadrilateral inscribed in a circle are supplementary

Theorem 12-5

- within a circle or in congruent circles - chords equidistant from the center are congruent - congruent chords are equidistant from the center

Theorem 12-4

- within a circle or in congruent circles - congruent central angles have congruent chords - congruent chords have congruent arcs - congruent arcs have congruent central angles

Theorem 12-2

- if a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle

Theorem 12-1

- if a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency

Theorem 12-7

- in a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord