U6 Vocabulary - Circles

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34 Terms

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central angle

an angle made of two radii whose vertex is at the center of the circle

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inscribed angle

an angle made of two intersecting chords whose vertex is on the circle

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arc length

the length of an arc or portion of the circumference

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sector

the portion of a circle enclosed by two radii and an arc

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circle

the set of points in a plane equidistant from the center of the circle

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circumference

the distance around the outside of a circle

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pi

the ratio of the circumference of a circle to its diameter

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chord

a segment whose endpoints lie on a circle

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minor arc

an arc of a circle whose measure is less than 180 degrees

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major arc

an arc of a circle whose measure is greater than 180 degrees

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area of a circle

the amount of space occupied by a circle (A=πr²)

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arc

a section of the circumference of a circle

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tangent

a line in the plane of a circle that intersects the circle in exactly one point

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secant

a line in the plane of the circle that intersects a circle in exactly two points

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inscribed circle

a circle inside a polygon in which all sides of the polygon are tangent to the circle

<p>a circle inside a polygon in which all sides of the polygon are tangent to the circle</p>
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radius

the distance from the center of a circle to any point on the circle

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diameter

the distance across a circle through its center

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point of tangency

the point at which a tangent line intersects a circle

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semicircle

half of a circle

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Chords and Arcs Theorem

In a circle, or in congruent circles, the arcs of congruent chords are congruent

<p>In a circle, or in congruent circles, the arcs of congruent chords are congruent</p>
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Chord Equidistance Theorem

In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

<p>In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.</p>
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Chord Perpendicular Bisector Theorem

A diameter (or radius) perpendicular to a chord bisects the chord and its arc

<p>A diameter (or radius) perpendicular to a chord bisects the chord and its arc</p>
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Quadrilateral inscribed in a circle

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary

<p>If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary</p>
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Central angle formula

angle=arc

<p>angle=arc</p>
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Inscribed angle formula

angle= 1/2(arc)

<p>angle= 1/2(arc)</p>
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tangent inscribed angle formula

angle = 1/2(arc)

<p>angle = 1/2(arc)</p>
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Formula to calculate angle formed inside of a circle by intersecting chords

(arc 1 + arc 2)/2

<p>(arc 1 + arc 2)/2</p>
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Formula to calculate angle formed outside of a circle by intersecting secants and tangents

angle = (big arc - small arc)/2

<p>angle = (big arc - small arc)/2</p>
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Formula to calculate chords' lengths if they intersect inside a circle

ab = cd

<p>ab = cd</p>
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Formula to calculate secant and another secant length if they have a common endpoint outside of the circle

whole x outside = whole x outside

<p>whole x outside = whole x outside</p>
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Formula to calculate secant or tangent length if they have a common endpoint outside of the circle

whole x outside = tangent squared

<p>whole x outside = tangent squared</p>
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Formula to calculate 2 tangents length if they have a common endpoint outside of the circle

If two tangent segments are drawn to a circle from an external point, then those segments are congruent.

<p>If two tangent segments are drawn to a circle from an external point, then those segments are congruent.</p>
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What relationship does a tangent line and a radius/diameter have?

If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency

<p>If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency</p>
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Equation of a circle

(x-h)²+(y-k)²=r², (h, k) is the center, r is the radius.

<p>(x-h)²+(y-k)²=r², (h, k) is the center, r is the radius.</p>