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Chapter 10.1 - 10.5
For Geometry
| Term | Definition |
|---|---|
| circle | A ______________ is the set of all points in a plane that are a given distance from a given point in the plane. |
| Center | The point that names the circle is the ________________ of the circle. Center |
| Radius | The distance from the center of a circle to the circle is the __________________. Radius |
| Diameter | A ___________ is the chord that passes through the center of the circle. Diameter |
| diameter | A ______ is equal in length to two radii |
| congruent | All radii of the same circle are _____. |
| r squared times Pi | The area of a circle = _____ |
| diameter times pi | The circumference of a circle = _____ |
| The % is the measure of the arc divided by 360. | The length of an arc = _____ %C |
| the area of a sector | 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. | concentric |
| A point is ____________ (in the ____________ of) a circle if its distance from the center is less than the radius | interior, inside |
| A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius | Outside, exterior |
| A point is _____a circle if its distance from the center is equal to the radius. | 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 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 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 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 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, secant |
| A ________________ is a line that intersects a circle at exactly _________ point. This point is called the _________________ ____ ________________ or point of contact. | tangent, one point, point of tangency or 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 | 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 part |
| If 2 tangent segments are drawn to a circle from an external point, then those segments are congruent | two tangent theorem |
| __________________________ ________________________ 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. Such a tangent is a _________________ __________ if it lies between the circles 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 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. | chord-chord angle |
| 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 angle |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent | secant tangent angle |
| 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 | 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 ____ 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 | center - arc inside - (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 | 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 | circumcenter |
| The center of a circle inscribed in a polygon is the _______________________ of the polygon. | 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 | the product of the measures of the segments of one chord is equal to the measures 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 measure 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 secant segment and its external part |
| The circumference of a circle is its | perimeter |
| The formula for the circumference of a circle is | C = pi * D |
| 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:
lesnib7
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