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9.2, Ch. 10
Axioms
| Question | Answer |
|---|---|
| A ______________ is the set of all points in a plane that are a given distance from a given point in the plane | (p 439, definition) Circle |
| The point that names the circle is the ________________ of the circle | Center |
| The distance from the center of a circle to the circle is the __________________ | Radius |
| A ___________ is the chord that passes through the center of the circle | Diameter |
| A ______ is equal in length to two radii | diameter |
| All radii of the same circle are _____ | (p 439, theorem) congruent |
| The circumference of a circle = _____ | dπ |
| The area of a circle = _____ | r2π |
| The length of an arc = _____ | %C |
| The area of a sector = _____ | The % is the % Ameasure of the arc divided by 360 |
| Two or more coplanar circles with the same center are called _____________________ circles | (p 439, definition) concentric |
| A point is ____________ (in the ____________ of) a circle if its distance from the center is less than the radius | (p 439, definition) Inside; interior |
| A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius | (p 439, definition) Outside exterior |
| A point is _____a circle if its distance from the center is equal to the radius | (p 440, definition) Equidistant |
| A _____ of a circle is a segment joining any 2 points on the circle | chord |
| A _____ of a circle is a chord that passes through the center of the circle | diameter |
| The distance from the center of a circle to a chord is the measure of the __________________ segment from the center to the chord | Perpendicular |
| "If a radius is perpendicular to a chord, then | it bisects the chord |
| If a radius of a circle bisects a chord that is not a diameter, then | It is perpendicular to the chord |
| The _____ of a chord passes through the center of a circle | Perpendicular bisector |
| If 2 chords of a circle are equidistant from the center of a circle, then ___ | The chords are congruent |
| If 2 chords of a circle are congruent, then ____ | They are equidistant |
| An _____ consists of 2 points on a circle and all points on the circle needed to connect the points by a single path | arc |
| The _____of an arc is the center of the circle of which the arc is a part | The unit is _____ Measure degrees |
| A _____ is an angle whose vertex is at the center of a circle | central |
| A _____is an arc whose points are on or between the sides of a central angle | Minor arc |
| A _____ is an arch whose points are on or outside of a central angle | Major arc |
| A _____ is an arc whose endpoints are the endpoints of a diameter | semicircle |
| The measure of a minor arc or a semicircle is _____the measure of the central angle that intercepts the arc | The same as |
| The measure of a major arc is 360 minus the measure of _______ _______________ ______ with the same endpoints | The minor arc |
| Two arcs are ________________ whenever they have the same measure and are parts of the same circle or congruent circles | congruent |
| "If 2 central angles of a circle (or of congruent circles) are congruent, then | the corresponding central angles are congruent |
| "If 2 arcs of a circle (or of congruent circles) are congruent, then | their intercepted arcs are congruent |
| "If 2 central angles of a circle (or of congruent circles) are congruent, then | the corresponding central angles are congruent |
| "If 2 chords of a circle (or of congruent circles) are congruent, then | then the corresponding chords are congruent |
| "If 2 arcs of a circle (or of congruent circles) are congruent, then | the corresponding arcs are congruent |
| "If 2 chords of a circle (or of congruent circles) are congruent, then | then the corresponding chords are congruent |
| A __________________ is a line that intersects a circle at exactly 2 points | (Every ______________ contains a chord of the circle |
| A tangent line is to the radius drawn to the point of contact | Perpendicular to a radius |
| "If a line is perpendicular to a radius at its outer endpoint, then | it is tangent to the circle |
| A ___________________________ ______________________________ is the part of a tangent line between the points of contact and a point outside the circle | Tangent segment |
| A __________________________ _______________________________ is the part of a secant line that joins a point outside the circle to the farther intersection point of the secant and the circle | secant segment |
| The ________________________ ____________________________ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point | external |
| "If 2 tangent segments are drawn to a circle from an external point, then | those segments are congruent |
| __________________________ ________________________ are circles that intersect each other at exactly one point | Tangent circles |
| Two circles are ________________________ _______________________ if each of the tangent circles lies outside the other | Externally tangent |
| Two circles are __________________________________ ______________________ if one of the tangent circles lies inside the other | internally tangent |
| An _____________________ ___________________ is an angle whose vertex is on a circle and whose sides are determined by 2 chords | Inscribed angle |
| A _________________________________ angle is an angle whose vertex is on a circle and whose sides are determined by a tangent and a chord that intersect at the tangent's point of contact | Tangent-chord |
| "The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is | one-half the measure of its intercepted arc |
| A ______________________________ angle is an angle formed by 2 chords that intersect inside a circle but not at the center | Chord-chord |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants | Secant-secant |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent | Secant-tangent |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents | Tangent-tangent |
| "If 2 inscribed or tangent-chord angles intercept the same arc, then | they are congruent |
| A polygon is __________________ ___________ a circle if all of its vertices lie on the circle | Inscribed polygon |
| A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle | circumscribed polygon |
| The center of a circle circumscribed about a polygon is the ____________________________ of the polygon | circumcenter |
| The center of a circle inscribed in a polygon is the _______________________ of the polygon | incenter |
| If a parallelogram is inscribed in a circle, | it must be a rectangle |
| If 2 chords of a circle intersect inside the circle, then | the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord |
| If a tangent segment and a secant segment are drawn from an external point to a circle, then | the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part |
| If 2 secant segments are drawn from an external point to a circle, then | the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part |
| The ____of a circle is its perimeter | circumference |
| The formula for the circumference of a circle is | c=pi(d) |
| The length of an arc is equal to the circumference of its circle times the fractional part of the circle determined by the arc | the circumference of its circle times the fractional part of the circle determined by the arc |
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