Examples, solutions, videos, worksheets, and activities to help Geometry students learn about theorems involving the chords and secants of a circle.
Chords and a Circle’s Center
A chord is a line segment whose endpoints are on a circle. If a chord passes through the center of the circle, it is called a diameter. Two important facts about a circle chord are that
(1) the perpendicular bisector of any chord passes through the center of a circle and
(2) congruent chords are the same distance (equidistant) from the center of the circle.
Chords of Circles, Congruent Chords and Arcs
Chords of circles. Congruent chords and their intercepted minor arcs (which are also congruent)
Chords of Circles, Perpendicular Bisectors
Chords of circles. Chords, perpendicular bisectors and diameters.
Chords of Circles, Congruent Chords and Equidistance
If chords are congruent, then they are equidistant from the center of the circle, and vice versa.
Radius, Chord, Diameter, and Secant
Students learn the definitions of a circle, a radius, a chord, a diameter, a secant
Segment Lengths in Circles
Students learn the following theorems related to chords, secants, and tangents. If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
Example involving the chord of a circle
Angle Measures in Circles
Students learn the following theorems related to chords, secants, and tangents. The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs. The measure of an angle formed by two secants drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.
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