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Chapter 10
| Question | Answer |
|---|---|
| A _______ is a set of all points in a plane that are a given distance from a given point in the plane. | Circle |
| The given point is the _________ of the circle... | Center |
| ...and the given distance is the _______. | Radius |
| 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 it |
| 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 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 interceoted 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 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 central 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; 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 | tangent to the circle |
| A ___________________________ ______________________________ is the part of a tangent line between the points of contact and a point outside the circle. | secant 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. | external part |
| The ________________________ ____________________________ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point. | segments are congruent |
| If 2 tangent segments are drawn to a circle from an external point, then | tangent circles |
| __________________________ ________________________ are circles that intersect each other at exactly one point. | internally tangent |
| Two circles are ________________________ _______________________ if each of the tangent circles lies outside the other. | common tangent, common internal tangent, common external tangent |
| Two circles are __________________________________ ______________________ if one of the tangent circles lies inside the other. | inscribed angle |
| A __________________ __________________ is a line tangent to two circles . Such a tangent is a _________________ __________________ __________________ if it lies between the circles or a ________________ _________________ __________________ if | 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 |
| The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is | 1/2 measure of intercepted arc |
| A ______________________________ angle is an angle formed by 2 chords that intersect inside a circle but not at the center. | secant secant |
| The measure of a chord-chord angle is | secant tangent |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants. | tangent tangent |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent. | 1/2 the difference of the measures of the intercepted arcs |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. | they are congruent |
| The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside the circle) is | (arc + arc)/2 |
| 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 | (arc + arc)/2 |
| If 2 inscribed or tangent-chord angles intercept congruent arcs, then | 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. | an inscribed polygon |
| A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle. | circumscribed |
| 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, | opp angle supp |
| If a parallelogram is inscribed in a circle, | rectangle |
| If 2 chords of a circle intersect inside the circle, then | (seg)(seg)=(seg)(seg) |
| If a tangent segment and a secant segment are drawn from an external point to a circle, then | tan^2=(sec)*(sec) |
| If 2 secant segments are drawn from an external point to a circle, then | out(whole)=out(whole) |
Created by:
joaquincbeard