Podcast
Questions and Answers
If a radius is perpendicular to a chord, which of the following statements must be true?
If a radius is perpendicular to a chord, which of the following statements must be true?
- It bisects the chord.
- It creates a tangent at the point of intersection.
- It bisects both the chord and its corresponding arc. (correct)
- It bisects the arc formed by the chord.
What conclusion can be drawn if a line bisects a chord and is perpendicular to it?
What conclusion can be drawn if a line bisects a chord and is perpendicular to it?
- Both B and C. (correct)
- The line is a radius or diameter of the circle.
- The line is a tangent to the circle.
- The line passes through the center of the circle.
In a given circle, two minor arcs are congruent. What can be definitively concluded about their corresponding chords?
In a given circle, two minor arcs are congruent. What can be definitively concluded about their corresponding chords?
- The chords are perpendicular.
- The chords intersect at the center of the circle.
- The chords are parallel.
- The chords are congruent. (correct)
If two chords in the same circle are equidistant from the center, what can be concluded?
If two chords in the same circle are equidistant from the center, what can be concluded?
Given circle with center O, chord AB is bisected at point M by radius OC. If $AB = 8$ and $OM = 3$, find the radius of the circle.
Given circle with center O, chord AB is bisected at point M by radius OC. If $AB = 8$ and $OM = 3$, find the radius of the circle.
In circle P, chords AB and CD are congruent. If the distance from P to AB is 5, what is the distance from P to CD?
In circle P, chords AB and CD are congruent. If the distance from P to AB is 5, what is the distance from P to CD?
A chord of length 16 is 6 units from the center of a circle. What is the length of the circle's radius?
A chord of length 16 is 6 units from the center of a circle. What is the length of the circle's radius?
In circle O, radius OC is perpendicular to chord AB. If $AB = 12$ and $OC = 10$, find the distance from O to the midpoint of AB.
In circle O, radius OC is perpendicular to chord AB. If $AB = 12$ and $OC = 10$, find the distance from O to the midpoint of AB.
If two circles are congruent, and each has a chord of length 8, what can be said about the arcs subtended by these chords?
If two circles are congruent, and each has a chord of length 8, what can be said about the arcs subtended by these chords?
Chord XY in a circle is 16 cm long, and the radius of the circle is 10 cm. Find the distance of the chord from the center of the circle.
Chord XY in a circle is 16 cm long, and the radius of the circle is 10 cm. Find the distance of the chord from the center of the circle.
If a diameter of a circle bisects a chord, which is NOT a diameter, then?
If a diameter of a circle bisects a chord, which is NOT a diameter, then?
Two chords, AB and CD, in a circle are congruent. If arc AB measures 75 degrees, what is the measure of arc CD?
Two chords, AB and CD, in a circle are congruent. If arc AB measures 75 degrees, what is the measure of arc CD?
In circle O, chord AB has length $2x$. The distance from O to AB is 3. If the radius of circle O is 5, what is the value of $x$?
In circle O, chord AB has length $2x$. The distance from O to AB is 3. If the radius of circle O is 5, what is the value of $x$?
If two chords in a circle intersect, forming two pairs of vertical angles, and one chord is bisected by the other, what can be concluded?
If two chords in a circle intersect, forming two pairs of vertical angles, and one chord is bisected by the other, what can be concluded?
Consider two concentric circles (circles sharing the same center). A chord in the larger circle is tangent to the smaller circle. If the chord's length is 24, what is the length of the radius of the larger circle if the radius of the smaller circle is 5?
Consider two concentric circles (circles sharing the same center). A chord in the larger circle is tangent to the smaller circle. If the chord's length is 24, what is the length of the radius of the larger circle if the radius of the smaller circle is 5?
A segment outside a circle is tangent to the circle. Another line from the same point intersects the circle at two locations forming a secant. Given the length of the tangent is 6 and the external part of the secant is 2, what is the length of the whole secant?
A segment outside a circle is tangent to the circle. Another line from the same point intersects the circle at two locations forming a secant. Given the length of the tangent is 6 and the external part of the secant is 2, what is the length of the whole secant?
In circle O, chords AB and CD intersect at point E inside the circle. If $AE = 4$, $EB = 6$, and $CE = 3$, find the length of ED.
In circle O, chords AB and CD intersect at point E inside the circle. If $AE = 4$, $EB = 6$, and $CE = 3$, find the length of ED.
In a circle, two parallel chords are on opposite sides of the center. If the chords have lengths 12 and 16, and the distance between them is 14, what is the radius of the circle?
In a circle, two parallel chords are on opposite sides of the center. If the chords have lengths 12 and 16, and the distance between them is 14, what is the radius of the circle?
Two circles with radii 5 and 8 have centers that are 13 units apart. A common tangent is drawn that touches both circles. What is the length of the common tangent segment between the two points of tangency?
Two circles with radii 5 and 8 have centers that are 13 units apart. A common tangent is drawn that touches both circles. What is the length of the common tangent segment between the two points of tangency?
Flashcards
Chord Bisector Theorem
Chord Bisector Theorem
If a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.
Equidistant Chords Theorem
Equidistant Chords Theorem
Chords are congruent if they are equidistant from the center.
Arc-Chord Congruence
Arc-Chord Congruence
In the same circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Study Notes
- Arcs and Chords Theorems
Chords Theorem 1
- If a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.
- If CD is perpendicular to AB, then AE is congruent to BE, and arc AD is congruent to arc BD
Chords Theorem 2
- The perpendicular bisector of a chord is the radius or diameter.
- If CD is perpendicular to AB and AE is congruent to BE, then CD is a radius (or diameter FD).
Arcs Theorem 1
- In the same circle or congruent circles, 2 minor arcs are congruent if their corresponding chords are congruent.
- If chord CD is congruent to chord AB, then arc CD is congruent to arc AB
Arcs Theorem 2
- In the same circle or congruent circles, chords are congruent if they are equidistant from the center.
- If EF = EG, then chord AB is congruent to chord CD.
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