| A | B |
|---|
| circle | is the set of all points in a plane that are equidistant from a given point, called the center |
| chord | is a segment whose endpoints are on the circle. |
| diameter | of a circle is a chord that passes through the center. d = 2r |
| radius | of a circle is a segment that has the center as one endpoint and a point on the circle as the other endpoint. r = (1/2)d |
| tangent | if a line intersects a circle at exactly at one point then the line is a tangent of the circle. |
| point of tangency | the point at which a tangent intersects the circle |
| secant | if a line intersects a circle at two points then the line is a secant of the circle |
| common tangent | a line that is tangent to two circles |
| common external tangents | a common tangent that does not intersect the segment that joins the centers of the circles is a common external tangent |
| common internal tangents | a common tangent that intersects the segment that joins the centers is a common internal tangent |
| concentric | circles that have the same center are concentric |
| Theorem 10.1: If a line is tangent to a circle | If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. |
| Theorem 10.2: In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle | In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle |
| Theorem 10.3: If two segments from the same exterior point are tangent to a circle, | If two segments from the same exterior point are tangent to a circle, then they are congruent |
| inscribed | a circle is inscribed if each side of the polygon is tangent to the circle |
| circumscribed | a circle is circumscribed about a polygon if each vertex lies on the circle |
| Postulate 21 Arc Addition Postulate | The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs. |
| Theorem 10.4: In the same circle, or in congruent circles, two arcs are congruent | In the same circle, or in congruent circles, two arcs are congruent if and only if their central angles are congruent. |
| Theorem 10.5: In the same circle or in congruent circles | In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. |
| Theorem 10.6: If a diameter of a circle is perpendicular to a chord | If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. |
| Theorem 10.7: If chord AB is a perpendicular bisector of another chord | If chord AB is a perpendicular bisector of another chord, then AB is a diameter. |
| Theorem 10.8: In the same circle or in congruent circles | In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center |
| Theorem 10.9: If an angle is inscribed in a circle | If an angle is inscribed in a circle, then it its measure is half of its intercepted arc. |
| Theorem 10.10: If two inscribed angles of a circle intercept the same arc | If two inscribed angles of a circle intercept the same arc, then the angles are congruent. |
| Theorem 10.11: An angle that is inscribed in a circle is a right angle if | An angle that is inscribed in a circle is a right angle if and only if its corresponding arc is a semicircle |
| Theorem 10.12: A quadrilateral can be inscribed in a circle if | A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. |
| Theorem 10.13: If a tangent and a chord intersect at a point on a circle, | If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is half the measure of its intercepted arc. |
| Theorem 10.14: If two chords intersect in the interior of a circle | If two chords intersect in the interior of a circle, then the measure of each angle is half the sum of the measure of the arcs intercepted by the angle and its vertical angle. |
| Theorem 10.15: If the tangent and a secant, two tangents, or two secants intersects in the exterior of a circle, then | If the tangent and a secant, two tangents, or two secants intersects in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of the intercepted arcs. |
