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20 Cards in this Set
- Front
- Back
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Sum of central angles
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The sum of the measures of the central angles of a circle with no interior points in common is 360.
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Definition of arc measure
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The measure of a minor arc is the measure of its central angle. the measure of a major arc is 360 - the measure of its central angle. The measure of a semicircle is 180.
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Arc addition postulate
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The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
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Corresponding chords arc congruency theorem
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In a circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
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Diameter chord perpendicularness
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In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.
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Chord congruency by distance from center
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In a circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
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Inscribed angle and intercepted arc relationship
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If an angle is inscribed in a circle, then the measure of the angle equals 1/2 the measure of its intercepted arc.
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Inscribed angle congruency by intercepted arcs
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If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent.
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Right inscribed angles by semicircle intercepts
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If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle.
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Inscribed quadrilateral angle relationships
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If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
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Radius-tangent angle relationship
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If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
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Converse of Radius-tangent angle relationship
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In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of a circle.
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Exterior point tangent relationship
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If two segments from the same exterior point are tangent to a circle, then they are congruent.
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Secant-tangent intercepted arc relationship
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If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one half the measure of the arc intercepted by the secant.
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http://goo.gl/UcnU1
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If two secants intersect in the interior of a circle, then the measure of an angle formed is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. The answer to the problem is D.
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http://goo.gl/y1gaR Arc DE = 60, Arc BC = 30
Find the measure of angle DAE |
If two secants, a secant an a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the positive difference of the measures of the intersected arcs. The answer is 15.
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http://goo.gl/hu7yT
AB = ? |
If two chords intersect at a circle, then the products of the measures of the segments of the chords are equal.
AB = CD |
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http://goo.gl/kXa6f
MN * NO = ? |
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
MP * PQ |
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http://goo.gl/LiOC8 Fill in the censored
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If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
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http://goo.gl/MqvNW
E(B + C) = ? |
If two secants are drawn to a circle from an exterior point, then the exterior part of one of the secants multiplied by the entire secant equals the exterior part of the other secant multiplied by the entire secant.
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