Circle Theorems

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28 Terms

1
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Minor Arc, Major Arc

Major arc >180

Minor arc < 180

<p>Major arc &gt;180</p><p>Minor arc &lt; 180</p>
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Central Angle

Central angle has the same measure with the arc

<p>Central angle has the same measure with the arc</p>
3
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Inscribed Angle

Inscribed angle is half the arc

<p>Inscribed angle is half the arc</p>
4
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Congruent Central Angles Theorem

Minor arcs congruent iff corresponding central angles are congruent

<p>Minor arcs congruent iff corresponding central angles are congruent</p>
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Tangent Line & Secant Line

Tangent line cuts the circle at 1 point Secant line cuts the circle at 2 points

<p>Tangent line cuts the circle at 1 point Secant line cuts the circle at 2 points</p>
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Tangent Line to Circle Theorem

Tangent line is perpendicular with radius

<p>Tangent line is perpendicular with radius</p>
7
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External Tangents Congruent Theorem

Tangent segments from external point are congruent

<p>Tangent segments from external point are congruent</p>
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Congruent Corresponding Chords Theorem

2 minor arcs congruent iff corresponding chords are congruent

<p>2 minor arcs congruent iff corresponding chords are congruent</p>
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Perpendicular Chord Bisector Theorem

Diameter perpendicular to chord then diameter bisects chord & its arc

<p>Diameter perpendicular to chord then diameter bisects chord &amp; its arc</p>
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Perpendicular Chord Bisector Converse

1 chord is perpendicular bisector with another chord then first chord is a diameter

<p>1 chord is perpendicular bisector with another chord then first chord is a diameter</p>
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Equidistance Chords Theorem

2 chords congruent iff distance from center to chord are congruent and perpendicular.

<p>2 chords congruent iff distance from center to chord are congruent and perpendicular.</p>
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Inscribed Right Triangle Theorem

The angle in a semicircle subtended by the diameter is a right angle

<p>The angle in a semicircle subtended by the diameter is a right angle</p>
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Inscribed Quadrilateral Theorem

Opposite angles quadrilateral sum = 180°

<p>Opposite angles quadrilateral sum = 180°</p>
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Inscribed Angles Theorem

Angles subtended by the same arc in a circle are equal.

<p>Angles subtended by the same arc in a circle are equal.</p>
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Tangent and Intersected Chord Theorem

Angle is 1/2 of intercepted arc

<p>Angle is 1/2 of intercepted arc</p>
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Angles Inside Circle Theorem

Angle is half of sum of the arcs

<p>Angle is half of sum of the arcs</p>
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Angles Outside Circle Theorem

Angle is half of the difference between the arcs

<p>Angle is half of the difference between the arcs</p>
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Circumscribed Angle Theorem

Circumscribed angle is equal to 180 minus the central angle

<p>Circumscribed angle is equal to 180 minus the central angle</p>
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Segments of Chords Theorem

Part x Part = part x part

<p>Part x Part = part x part</p>
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Segments of Secants Theorem

(Outside) part x whole = (Outside) part x whole

<p>(Outside) part x whole = (Outside) part x whole</p>
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Segments of Secants and Tangents Theorem

tangent² = Part x Whole (secant)

<p>tangent² = Part x Whole (secant) </p>
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Circumference of Circle

C = đťť…d = 2đťť…r

<p>C = <span>đťť…d</span> = 2<span>đťť…r</span></p>
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Arc Length

Arc length of AB.

_______________. = mAB/360°

2đťť…r

Or

Arc length of AB = mAB/360° x 2𝝅r

<p>Arc length of AB.       </p><p>_______________.     =  mAB/360° </p><p>2<span>𝝅r </span></p><p>Or</p><p>Arc length of AB = mAB/360° x 2<span>𝝅</span>r</p>
24
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Area of Circle

A = 𝝅r²

<p>A = <span>𝝅r²</span></p>
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Area of a Sector

Area of sector APB/ 𝝅r² = mAB/360°

Or

Area of sector APB = mAB/360° x 𝝅r²

<p>Area of sector <em>APB/ </em>𝝅r² = mAB/360°</p><p>Or </p><p>Area of sector <em>APB</em> = mAB/360° x 𝝅r²</p>
26
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Standard Equation of Circle

Center (h,k) and radius r

(x — h)² + (y — k)² = r²

<p>Center (h,k) and radius r</p><p>(x — h)² + (y — k)² = r²</p>
27
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Radians to Degrees

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Degrees to Radians

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