Circle Relationships: Angles, Radii, and Chords - Geometry
Card 1 of 30
What is the measure of a tangent-chord angle if its intercepted arc measures $148^\circ$?
What is the measure of a tangent-chord angle if its intercepted arc measures $148^\circ$?
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$74^\circ$. Use $\frac{1}{2} \times 148° = 74°$.
$74^\circ$. Use $\frac{1}{2} \times 148° = 74°$.
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What is the exterior angle measure if a tangent and secant intercept arcs of $190^\circ$ and $70^\circ$?
What is the exterior angle measure if a tangent and secant intercept arcs of $190^\circ$ and $70^\circ$?
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$60^\circ$. Use $\frac{1}{2}(190° - 70°) = \frac{120°}{2} = 60°$.
$60^\circ$. Use $\frac{1}{2}(190° - 70°) = \frac{120°}{2} = 60°$.
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What is the relationship between a central angle measure and its intercepted arc measure?
What is the relationship between a central angle measure and its intercepted arc measure?
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They are equal: $m\angle AOB = m\overset{\frown}{AB}$. A central angle equals its intercepted arc by definition.
They are equal: $m\angle AOB = m\overset{\frown}{AB}$. A central angle equals its intercepted arc by definition.
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What is the relationship between an inscribed angle measure and its intercepted arc measure?
What is the relationship between an inscribed angle measure and its intercepted arc measure?
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$m\angle ACB = \frac{1}{2}m\overset{\frown}{AB}$. An inscribed angle is half its intercepted arc.
$m\angle ACB = \frac{1}{2}m\overset{\frown}{AB}$. An inscribed angle is half its intercepted arc.
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What conclusion can you make if a chord is closer to the center than another chord (same circle)?
What conclusion can you make if a chord is closer to the center than another chord (same circle)?
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The closer chord is longer. Shorter distance from center means longer chord length.
The closer chord is longer. Shorter distance from center means longer chord length.
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What is the relationship between a diameter perpendicular to a chord and that chord?
What is the relationship between a diameter perpendicular to a chord and that chord?
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It bisects the chord (and its intercepted arc). A perpendicular diameter divides the chord into equal parts.
It bisects the chord (and its intercepted arc). A perpendicular diameter divides the chord into equal parts.
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What is the relationship between the perpendicular bisector of a chord and the circle’s center?
What is the relationship between the perpendicular bisector of a chord and the circle’s center?
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It passes through the center. The perpendicular bisector of any chord passes through the center.
It passes through the center. The perpendicular bisector of any chord passes through the center.
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What is the exterior angle measure if two secants intercept arcs of $250^\circ$ and $150^\circ$?
What is the exterior angle measure if two secants intercept arcs of $250^\circ$ and $150^\circ$?
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$50^\circ$. Use $\frac{1}{2}(250° - 150°) = \frac{100°}{2} = 50°$.
$50^\circ$. Use $\frac{1}{2}(250° - 150°) = \frac{100°}{2} = 50°$.
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What is the measure of an inscribed angle that intercepts an arc of $180^\circ$?
What is the measure of an inscribed angle that intercepts an arc of $180^\circ$?
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$90^\circ$. A $180°$ arc (semicircle) creates a $90°$ inscribed angle.
$90^\circ$. A $180°$ arc (semicircle) creates a $90°$ inscribed angle.
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What is the measure of a central angle that intercepts an arc of $35^\circ$?
What is the measure of a central angle that intercepts an arc of $35^\circ$?
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$35^\circ$. A central angle equals its intercepted arc measure.
$35^\circ$. A central angle equals its intercepted arc measure.
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What is the measure of an inscribed angle if the intercepted arc is $35^\circ$?
What is the measure of an inscribed angle if the intercepted arc is $35^\circ$?
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$17.5^\circ$. Use $\frac{1}{2} \times 35° = 17.5°$.
$17.5^\circ$. Use $\frac{1}{2} \times 35° = 17.5°$.
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What is the measure of the intercepted arc if an inscribed angle is $17.5^\circ$?
What is the measure of the intercepted arc if an inscribed angle is $17.5^\circ$?
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$35^\circ$. The arc is twice the inscribed angle: $2 \times 17.5° = 35°$.
$35^\circ$. The arc is twice the inscribed angle: $2 \times 17.5° = 35°$.
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What conclusion can you make if two inscribed angles intercept the same arc $\overset{\frown}{AB}$?
What conclusion can you make if two inscribed angles intercept the same arc $\overset{\frown}{AB}$?
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They are congruent. Inscribed angles on the same arc are always equal.
They are congruent. Inscribed angles on the same arc are always equal.
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What conclusion can you make if two central angles intercept congruent arcs in the same circle?
What conclusion can you make if two central angles intercept congruent arcs in the same circle?
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The central angles are congruent. Equal arcs create equal central angles in the same circle.
The central angles are congruent. Equal arcs create equal central angles in the same circle.
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What conclusion can you make if two chords in the same circle are congruent?
What conclusion can you make if two chords in the same circle are congruent?
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They are equidistant from the center. Equal chords are always equidistant from the center.
They are equidistant from the center. Equal chords are always equidistant from the center.
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What is the relationship between equal central angles and their intercepted chords?
What is the relationship between equal central angles and their intercepted chords?
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Equal central angles intercept congruent chords. Equal central angles create equal chords in the same circle.
Equal central angles intercept congruent chords. Equal central angles create equal chords in the same circle.
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What is the relationship between equal inscribed angles and their intercepted arcs?
What is the relationship between equal inscribed angles and their intercepted arcs?
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Equal inscribed angles intercept congruent arcs. Equal inscribed angles create equal arcs in the same circle.
Equal inscribed angles intercept congruent arcs. Equal inscribed angles create equal arcs in the same circle.
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What is the relationship between equal inscribed angles and their intercepted chords?
What is the relationship between equal inscribed angles and their intercepted chords?
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Equal inscribed angles intercept congruent chords. Equal inscribed angles create equal chords in the same circle.
Equal inscribed angles intercept congruent chords. Equal inscribed angles create equal chords in the same circle.
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What is the relationship between congruent arcs and their corresponding chords in the same circle?
What is the relationship between congruent arcs and their corresponding chords in the same circle?
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Congruent arcs have congruent chords. Equal arcs are created by equal chords in the same circle.
Congruent arcs have congruent chords. Equal arcs are created by equal chords in the same circle.
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What is the relationship between congruent chords and their intercepted arcs in the same circle?
What is the relationship between congruent chords and their intercepted arcs in the same circle?
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Congruent chords intercept congruent arcs. Equal chords create equal arcs in the same circle.
Congruent chords intercept congruent arcs. Equal chords create equal arcs in the same circle.
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What is the name for a segment from the center of a circle to a point on the circle?
What is the name for a segment from the center of a circle to a point on the circle?
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A radius. A radius connects the center to any point on the circle.
A radius. A radius connects the center to any point on the circle.
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What is the name for a chord that passes through the center of the circle?
What is the name for a chord that passes through the center of the circle?
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A diameter. A diameter is a special chord passing through the center.
A diameter. A diameter is a special chord passing through the center.
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What is the name for a segment whose endpoints lie on a circle?
What is the name for a segment whose endpoints lie on a circle?
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A chord. A chord connects two points on the circle's circumference.
A chord. A chord connects two points on the circle's circumference.
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What is the measure of an inscribed angle that intercepts a diameter $\overline{AB}$?
What is the measure of an inscribed angle that intercepts a diameter $\overline{AB}$?
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$90^\circ$. By Thales' theorem, any inscribed angle on a diameter is $90°$.
$90^\circ$. By Thales' theorem, any inscribed angle on a diameter is $90°$.
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What is the measure of an inscribed angle if the corresponding central angle is $110^\circ$?
What is the measure of an inscribed angle if the corresponding central angle is $110^\circ$?
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$55^\circ$. The inscribed angle is half the central angle: $\frac{110°}{2} = 55°$.
$55^\circ$. The inscribed angle is half the central angle: $\frac{110°}{2} = 55°$.
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What is the measure of the central angle if an inscribed angle intercepting the same arc is $28^\circ$?
What is the measure of the central angle if an inscribed angle intercepting the same arc is $28^\circ$?
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$56^\circ$. The central angle is twice the inscribed angle: $2 \times 28° = 56°$.
$56^\circ$. The central angle is twice the inscribed angle: $2 \times 28° = 56°$.
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What is the measure of the intercepted arc if an inscribed angle measures $37^\circ$?
What is the measure of the intercepted arc if an inscribed angle measures $37^\circ$?
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$74^\circ$. The arc is twice the inscribed angle: $2 \times 37° = 74°$.
$74^\circ$. The arc is twice the inscribed angle: $2 \times 37° = 74°$.
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What is the measure of an inscribed angle that intercepts an arc of $86^\circ$?
What is the measure of an inscribed angle that intercepts an arc of $86^\circ$?
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$43^\circ$. Use $\frac{1}{2} \times 86° = 43°$.
$43^\circ$. Use $\frac{1}{2} \times 86° = 43°$.
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What is the measure of an inscribed angle that intercepts a major arc of $240^\circ$?
What is the measure of an inscribed angle that intercepts a major arc of $240^\circ$?
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$120^\circ$. Use $\frac{1}{2} \times 240° = 120°$.
$120^\circ$. Use $\frac{1}{2} \times 240° = 120°$.
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What is the measure of a central angle that intercepts a semicircle?
What is the measure of a central angle that intercepts a semicircle?
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$180^\circ$. A semicircle is exactly half the circle, which is $180°$.
$180^\circ$. A semicircle is exactly half the circle, which is $180°$.
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