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Chapter 10 Circle
Chapter 10 Circles Studyguide
| Question | Answer |
|---|---|
| Circle | A ______________ is the set of all points in a plane that are a given distance from a given point in the plane. |
| Diameter | A ___________ is the chord that passes through the center of the circle. |
| dπ | The circumference of a circle = _____ |
| r2π | The area of a circle = _____ |
| %C The % is the measure of the arc divided by 360. | The length of an arc = _____ |
| % A The % is the measure of the arc divided by 360. | The area of a sector = _____ |
| concentric | Two or more coplanar circles with the same center are called _____________________ circles |
| Inside, interior | A point is ___ (in the ___ of) a circle if its distance from the center is less than the radius |
| Outside exterior | A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius. |
| Equidistant | A point is _____a circle if its distance from the center is equal to the radius. |
| Perpendicular | The distance from the center of a circle to a chord is the measure of the __________________ segment from the center to the chord. |
| It bisects it | If a radius is perpendicular to a chord, then |
| It is perpendicular to the chord | If a radius of a circle bisects a chord that is not a diameter, then |
| Perpendicular bisector | The _____ of a chord passes through the center of a circle. |
| The chords are congruent | If 2 chords of a circle are equidistant from the center of a circle, then ___. |
| Measure, degrees | The _____of an arc is the center of the circle of which the arc is a part. The unit is _____ |
| central | A _____ is an angle whose vertex is at the center of a circle. |
| minor arc | A _____is an arc whose points are on or between the sides of a central angle. |
| Major arc | A _____ is an arch whose points are on or outside of a central angle. |
| The minor arc | The measure of a major arc is 360 minus the measure of _______ _______________ ______ with the same endpoints. |
| their intercepted arcs are congruent | If two central angles of a circle are congruent, then |
| the corresponding central angels ( or arcs) are congruent | If 2 chords of a circle are congruent, then |
| Secant | A ______ is a line that intersects a circle at exactly 2 points. (Every _____ contains a chord of the circle |
| Tangent, point of tangency, point of contact | A ________________ is a line that intersects a circle at exactly _________ point. This point is called the _________________ ____ ________________ or point of contact. |
| Perpendicular | A tangent line is ____ to the radius drawn to the point of contact. |
| It is tangent to the circle | If a line is perpendicular to a radius at its outer endpoint, then |
| those segments are congruent. (Two-Tangent Theorem) | If 2 tangent segments are drawn to a circle from an external point, then |
| Inscribed angle | An _____________________ ___________________ is an angle whose vertex is on a circle and whose sides are determined by 2 chords |
| Tangent-chord 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. |
| one half the measure of its intercepted arc | The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is |
| Chord-Chord angle | A ______________________________ angle is an angle formed by 2 chords that intersect inside a circle but not at the center. |
| 1/2 the sum of the measure of the arcs intercepted by the chord chord angle and its vertical angle | The measure of a chord-chord angle is |
| secant-secant | A ________ angle is an angle whose vertex is outside a circle and whose sides are determined b 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 |
| tangent-tangent | A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. |
| 1/2 the difference of the measures of the intercepted arcs | The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside the circle) is |
| they are congruent | If 2 inscribed or tangent-chord angles intercept the same arc, then |
| they are congruent | If 2 inscribed or tangent-chord angles intercept congruent arcs, then |
| right angle | An angle inscribed in a semi- circle is a ____________________ ___________________. |
| 180 | The sum of the measures of a tangent-tangent angle and is minor arc is |
| Inscribed in | A polygon is __________________ ___________ a circle if all of its vertices lie on the circle. |
| circumscribed about | A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle. |
| circumcenter | The center of a circle circumscribed about a polygon is the ____________________________ of the polygon. |
| Incenter | The center of a circle inscribed in a polygon is the _______________________ of the polygon. |
| its opposite angles are supplementary | If a quadrilateral is inscribed in a circle, |
| it must be a rectangle | If a parallelogram is inscribed in a circle, |
| the product of the measures of the segs of one chord is equal to the product of the measures of the segs of the other chord | If 2 chords of a circle intersect inside the circle, then |
| the square of the measure of the tangent seg is equal to the product of the measure of the entire secant segment and its external part | If a tangent seg and a secant seg are drawn from an external point to a circle, then |
| the product of the measures of one secant seg and its external part is equal to the product of the measures of the other secant seg and its external part | If 2 secant segments are drawn from an external point to a circle, then |
| circumference | The ____ of a circle is its perimeter. |
| (Pi)(d) | The formula for the circumference of a circle is |
| circumference times the fractional part of the circle determined by the arc | The length of an arc is equal to |
Created by:
JamesBuisson
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