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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 |
| 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 π |
| The area of a circle = _____ | r2 π |
| 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 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) | on the circle |
| 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. | perpindicular |
| 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 | 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 central angles are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent then | 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 contact or 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 | its 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). | common 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 | one half the measurement of its intercepted arc |
| 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 |
| A ______________________________ angle is an angle formed by 2 chords that intersect inside a circle but not at the center. | chord-chord |
| The measure of a chord:chord angle is | one half the sum of the two intersepted arcs |
| 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 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: |
| If the vertex of the angle is center of the circle | then it is equal to the Arc |
| If the vertex of the angle is IN the circle | then it is equal to (Arc + arc)/2 |
| If the vertex of the angle is ON the circle | then it is equal to (arc)/2 |
| If the vertex of the angle is OUT the circle | then it is equal to (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 ____________________ ___________________. | is a right angle |
| The sum of the measures of a tangent:tangent angle and its minor arc is __________________. | 180 degrees |
| 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. | incenter |
| If a quadrilateral is inscribed in a circle | the 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 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 tangent segment is equal to the product of the measures 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 segment and its external part is equal to the product of the measures of the other segment and its external part |
| 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 | the circumference of its circle times the fractional part of the circle determined by the arc |
Created by:
JoeSmu
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