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Chapter 10
| 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 edge of the circle is the ______ | radius |
| A _______ is the chord that passses 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 = | pi*diameter |
| The area of a circle | r^2*pi |
| The length of an arc = | 2πr (θ/360) |
| The area of a sector = ____ | The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2 |
| Two or more coplanar circles with the same center are called _______ circles (p439 definition) | concentric circles |
| 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 _____ a circle if its distance from the center is equal to the radius (p. 439) definition | equidistant to |
| A _____ of a circle is a chord that passes through the center of the circle | chord |
| 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 that 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 ________ | they are congruent |
| If 2 chords of a circle are congruent, then ______ | they are equidistant from the center of a circle |
| 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 angle |
| A ______ is an arc whose points are on or between the sides of a central angle | minor arc |
| A ______ is an arc 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 orr 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 intercepted arcs are congruent |
| If 2 arcs of a circle (or 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 circle) 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; point of tangency;point of contact |
| A tangent line is _________ to the radius | 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 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 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 |
| The measure of an inscribed angle or a tangent-chord angle (vertex on a circle) is _____________ | 1/2 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 | inscribed |
| 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 decided 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 two 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 | they are congruent |
| if the vertex of the angle is in the circle, then use this formula to find the angle's measure | (arc+arc)/2 |
| if the vertex of the angle is in the center circle, then use this formula to find the angle's measure | arc |
| if the vertex of the angle is on the circle, then use this formula to find the angle's measure | arc/2 |
| if the vertex of the angle is out of the circle, then use this formula to find the angle's measure | (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 | 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, _______________ | then its opposite angles are supplementary |
| If a parallelogram is inscribed in a circle, ____________ | then it must be a rectangle |
| If 2 chords of a circle intersect inside the circle, then _________________________________ | the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord; (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) |
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Simim21