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Geo Ch.10 Conner Roe
Axioms
| 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 = _____ | Diameter* pi or twice radius * pi |
| The area of a circle = _____ | radius squared times pi |
| The length of an arc = _____ | %C where the % is the measure of the arc divided by 360 |
| The area of a sector = _____ | % A where 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 | The radius bisects the cord |
| 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 to the center of the 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. | measure of the arc |
| A _____ is an angle whose vertex is at the center of a circle. central | central angle |
| 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. | semi circle |
| The measure of a minor arc or a semicircle is _____the measure of the central angle that intercepts the arc. | equal to |
| 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 chords are congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent then | their central angles are congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent then | their chords are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent then | they are equidistant from the center of the circle |
| If 2 arcs of a circle (or of congruent circles) are congruent then | their corresponding chords are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent then | their corresponding arcs are congruent |
| A __________________ is a line that intersects a circle at exactly 2 points. | secant |
| A ________________ is a line that intersects a circle at exactly _________ point. | tangent, one tangent point |
| A tangent line is | the radius drawn to the point of contact. |
| 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 point |
| If 2 tangent segments are drawn to a circle from an external point then | they 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. | tan-chord angle |
| The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is | 1/2 the measure of the implied arc |
| 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 | 1/2 the sum of the measure of the two arcs that are inscribed by the chord chord angle |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants. | secant tangent |
| 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 angle |
| The measure of a secant-secant angle a secant-tangent angle or a tangent-tangent angle (vertex outside the circle) is | 1/2 the difference of the measure of the two inscribed arc by the secant secant angle |
| If 2 inscribed or tangent-chord angles intercept the same arc then | the angles are congruent |
| Center Arc | inscribed by a central angle |
| IN (Arc + arc)/2 | chord chord arc |
| ON (arc)/2 | inscribed angle |
| OUT (arc-arc)/2 | secant secant arc |
| If 2 inscribed or tangent-chord angles intercept congruent arcs then | the angles 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 degrees |
| A polygon is __________________ ___________ a circle if all of its vertices lie on the circle. | inscribed |
| 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 | then opposite angles are supplementary |
| If a parallelogram is inscribed in a circle | it is a rectangle |
| If 2 chords of a circle intersect inside the circle then | the products of the divided parts of each chord are equal |
| If a tangent segment and a secant segment are drawn from an external point to a circle then | the measure of the tangent squared is equal to the measure of the external part of the secant and the secants measure multiplied are equal |
| If 2 secant segments are drawn from an external point to a circle then | the products of the measure of the external part of each secant segment to the measure of the secant are equal |
| The of a circle is its perimeter. | circumfrence |
| The formula for the circumference of a circle is . | diameter*pi |
| The length of an arc is equal to | the measure of the arc over 360 degrees times circumfrence |
Created by:
CJRoeder
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