10.3 Chords of a circle
Congruent Corresponding Chords Theorem and the Equidistant Chords Theorem
Find the measure of arc CD and arc EF. Find the length the chords are from the center.
To find the measure of arc CD and arc EF:
Click the circle tool and select "Circular Arc"
Click the center, then click each endpoint of the chord
Look at the left hand column to find the arc measure
Repeat with the other chord (BE SURE TO SELECT CORRESPONDING POINTS WHEN FINDING THE SECOND ARC MEASURE)
Change the length of chords CD and find the arc measures of arc CD and arc EF.
Move the blue endpoints of chord CD and look at the arc measures in the left hand column.
What is the measure of arc CD and arc EF
What happened to the arc measures when you changed the lengths of chords CD and EF?
If two chords of the same circle are congruent then what two conclusions can we make?
Points C, D, and E represent three apple trees in a yard. Where would you place a sprinkler so that the trees are equidistant from the sprinkler?
The perpendicular bisector of a chord always goes through what point of the circle.
Perpendicular Chord Bisector Theorem
Construct a diameter of the circle. Draw a chord such that it is perpendicular to the diameter. Find the lengths of each segment of the chord. Find the measure of the arc created by the endpoints of the chord.
If a diameter is perpendicular to a chord then the diameter will __________________. (complete the statement)
Perpendicular Chord Bisector Theorem Converse
Construct a chord to the given circle. Construct a perpendicular bisector of a chord. Move the chord around and see what happens to the perpendicular bisector.
If one chord of a circle is a perpendicular bisector of another chord, then the first chord is a ____________.
In general any line, ray, or segment going through the center of a circle and perpendicular to a chord will bisect the chord and the arc the chord creates.