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Geometry ch. 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 | 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 = _____ | d(pi) |
| The area of a circle = _____ | r2 |
| The length of an arc = _____ | %C |
| The % is the measure of the arc divided by 360. | Arc/360 |
| The area of a sector = _____ | % A |
| 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) 439 D | 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 440 D | outside, exterior |
| A point is _____a circle if its distance from the center is equal to the radius. (p 440, definition) Equidistant 440 D | on |
| A _____ of a circle is a segment joining any 2 points on the circle. chord 440 D | chord |
| A _____ of a circle is a chord that passes through the center of the circle. diameter 440 D | diameter |
| The distance from the center of a circle to a chord is the measure of the __________________ segment from the center to the chord. 441 D | perpendicular |
| If a radius is perpendicular to a chord, then | 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 441 T75 |
| The _____ of a chord passes through the center of a circle. 441 T76 | perpendicular bisector |
| If 2 chords of a circle are equidistant from the center of a circle, then ___. | The chords are congruent 446 T77 |
| 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 450 D | arc |
| The _____of an arc is the center of the circle of which the arc is a part. The unit is _____ Measure degrees 450 D | center |
| A _____ is an angle whose vertex is at the center of a circle. central 450 D | central angle |
| A _____is an arc whose points are on or between the sides of a central angle. 451 D | minor acr |
| A _____ is an arch whose points are on or outside of a central angle. 451 D | major arc |
| A _____ is an arc whose endpoints are the endpoints of a diameter. semicircle 451 D | semicircle |
| The measure of a minor arc or a semicircle is _____the measure of the central angle that intercepts the arc. 451 D | the same as |
| The measure of a major arc is 360 minus the measure of _______ _______________ ______ with the same endpoints. 451 D | the minor arc |
| Two arcs are ________________ whenever they have the same measure and are parts of the same circle or congruent circles. 452 D | 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 conguent |
| 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.) 459 D | secant |
| A ________________ is a line that intersects a circle at exactly _________ point. This point is called the _________________ ____ ________________ or point of contact. 459 D | tangent, one, point of tangency, |
| A tangent line is to the radius drawn to the point of contact. 459 P | 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. 460 D | 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. 460 D | secant segment |
| The ________________________ ____________________________ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point. 460 D | 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. 460 D | tangent circles |
| Two circles are ________________________ _______________________ if each of the tangent circles lies outside the other. 460 D | externally tangent |
| Two circles are __________________________________ ______________________ if one of the tangent circles lies inside the other. 460 D | 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 | common tangent, common internal tangent |
| An _____________________ ___________________ is an angle whose vertex is on a circle and whose sides are determined by 2 chords. 469 D | 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. 469 D | 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. 470 D | chord-chord angel |
| The measure of a chord-chord angle is 470 T87 | is one half the sum of the measures of the arcs intercepted by the chord-chord angel and its vertical angle |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants. 471 D | secant-secant |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent. 471 D | secant tangent |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. 471 D | 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 |
| Complete the chart below. In class, I provided a summary on the board; this is how I anticipate you will complete the chart. (Hint: I pointed out the top of page 472 when I completed it in class.) | |
| If the vertex of the angle is ____ the circle Then use this formula to find the angle’s measure: | in a+b/2 |
| Center Arc | vertex at center=equals 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 ____________________ ___________________. 479 T90 | tangent chord angle |
| The sum of the measures of a tangent-tangent angle and its minor arc is __________________. 480 T91 | right angle |
| A polygon is __________________ ___________ a circle if all of its vertices lie on the circle. 480 T92 | circumscribed in |
| A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle. 486 D | circumscribed about |
| The center of a circle circumscribed about a polygon is the ____________________________ of the polygon. 486 D | 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 | 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. (seg)(seg)=(seg)(seg) |
| If a tangent segment and a secant segment are drawn from an external point to a circle, then | (tang.)^2=(out)((in) of secant (out)^2 =(in)(out) |
| If 2 secant segments are drawn from an external point to a circle, then | (out)(whole)=(out)(whole) |
| The of a circle is its perimeter. 493 T97 | circumference |
| The formula for the circumference of a circle is . 499 D | c=pi(d) |
| The length of an arc is equal to | is equal to the circumference of its circle times the fractional part of the circle determined by the arc. Arc=(arc/360)piD |
Created by:
beinej27