click below

click below

Normal Size Small Size show me how

# 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 | 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 _____. | Congruent |

The circumference of a circle = _____. | dπ |

The area of a circle = _____. | r²π |

The length of an arc = _____. | %C The % is the measure of the arc divided by 360. |

The area of a sector = _____. | % A The % is the measure of the arc divided by 360. |

Two or more coplanar circles with the same center are called _____________________ circles. | Concentric |

A point is ____________ (in the ____________ of) a circle if its distance from the center is less than the radius. | Inside, interior |

A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius. | Outside, exterior |

A point is _____a circle if its distance from the center is equal to the radius. | 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 _______________________________________ | their intercepted arcs are congruent |

If 2 arcs of a circle (or of congruent circles) are congruent, then __________________________________________________ | the corresponding central angles 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 _______________________________________________ | the corresponding central angles are congruent |

If 2 arcs of a circle (or of congruent circles) are congruent, then __________________________________________________ | the corresponding chords are congruent |

If 2 chords of a circle (or of congruent circles) are congruent, then _______________________________________________ | the corresponding arcs are congruent |

A __________________ is a line that intersects a circle at exactly 2 points. (Every ______________ contains a chord of the circle.) | secant |

A ________________ is a line that intersects a circle at exactly _________ point. This point is called the _________________ ____ ________________ or point of contact. | tangent, one, point of tangency or point of contact |

A tangent line is ____________________________________ to the radius drawn to the point of contact. | perpendicular |

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 part |

If 2 tangent segments are drawn to a circle from an external point, then ________________________________________ | those segments are congruent (Two-Tangent Theorem) |

__________________________ ________________________ 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 |

A _ _is a line tangent to two circles (not necessarily at the same point). | common tangent |

Such a tangent is a _ _ _ if it lies between the circles (intersects the segment joining the centers) or a _ _ _ if it is not between the circles (does not intersect the segment joining the centers). | common internal tangent, common external 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 angle |

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 angle |

The measure of a chord-chord angle is _________________________________ | one-half the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle |

A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants. | secant-secant angle |

A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent. | secant-tangent angle |

A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. | tangent-tangent angle |

The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside the circle) is ______________________________ | one-half the difference of the measures of the intercepted arcs |

If 2 inscribed or tangent-chord angles intercept the same arc, then _____________________________________ | they are congruent |

If the vertex of the angle is ____ the circle Then use this formula to find the angle’s measure: Center Arc IN (Arc + arc)/2 ON (arc)/2 OUT (arc-arc)/2 | |

If 2 inscribed or tangent-chord angles intercept congruent arcs, then _____________________ | they are congruent |

An angle inscribed in a semi- circle is a ____________________ ___________________. | right angle |

The sum of the measures of a tangent-tangent angle and its minor arc is __________________. | 180 |

A polygon is __________________ ___________ a circle if all of its vertices lie on the circle. | inscribed in |

A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle. | circumscribed about |

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 quadrilateral is inscribed in a circle, ____________________________ | its opposite angles are supplementary |

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 (chord-chord power theorem) |

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 (tangent-secant power theorem) |

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 (secant-secant power theorem) |

The ______________________________________ of a circle is its perimeter. | circumference |

The formula for the circumference of a circle is _________________ | C=πd |

The length of an arc is equal to ________________ | to the circumference of its circle times the fractional part of the circle determined by the arc |