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Chapt 10 Axioms
Circles
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 % 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. (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. | same |
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 chords 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, 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 the tangent of 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 |
If 2 central angles of a circle (or of congruent circles) are congruent, then . | their intercepting arcs 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 . | 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, point of tangency |
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 |
__________________________ ________________________ 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). 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 | common tangent, 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 measured sure 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 |
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 |
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 . | then they are congruent |
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 |
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 measure 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 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 . | (pi)diameter |
The length of an arc is equal to . | the circumference of its circle times the fractional part of the circle determined by the arc |