Circles, II
Circles, IIChordsArcs
Definition ArcA central angle separates the circle into two
parts, each of which is an arc. The measure of each arc is related
to the measure of its central angle. Arcs
Arc Addition PostulateThe measure of an arc formed by two
adjacent (neighboring) arcs is the sum of the measures of the two
arcs.
Example 1 Measures of ArcsCompute the measurement of arc BE
Example 1 Measures of ArcsCompute the measurement of arc BE
Example 1 Measures of ArcsCompute the measurement of arc BE
Example 1 Measures of ArcsCompute the measurement of arc BE
Example 2 Measures of ArcsCompute the measurement of arc CE
Example 2 Measures of ArcsCompute the measurement of arc CE
Arc CE is a minor arc
Example 2 Measures of Arcs
Example 2 Measures of Arcs
Example 3 Measures of ArcsCompute the measurement of arc ACE
Example 3 Measures of ArcsCompute the measurement of arc ACE
Arc ACE is a major arc
Example 3 Measures of Arcs
Example 3 Measures of Arcs
CW Arcs Arcs and Chords 2 TheoremsIn a circle or in congruent
circles, two minor arcs are congruent if and only if their
corresponding chords are congruent.
Arcs and Chords 2 TheoremsIn a circle or in congruent circles,
two minor arcs are congruent if and only if their corresponding
chords are congruent.
Arcs and Chords 2 TheoremsIn a circle or in congruent circles,
two minor arcs are congruent if and only if their corresponding
chords are congruent.
Arcs and Chords 2 TheoremsIn a circle or in congruent circles,
two minor arcs are congruent if and only if their corresponding
chords are congruent.
Arcs and Chords 2 TheoremsIn a circle, if a diameter (or radius)
is perpendicular to a chord, then it bisects (cut in half) the
chord and its arc.
Arcs and Chords 2 TheoremsIn a circle, if a diameter (or radius)
is perpendicular to a chord, then it bisects (cut in half) the
chord and its arc.
Example 1Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Example 1Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Example 1Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Example 1Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Draw segment CO, CO =
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Draw segment CO, CO = 13
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Draw segment CO, CO = 13 CX = 12, by the second theorem.
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Draw segment CO, CO = 13 CX = 12, by the second theorem.
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Draw segment CO, CO = 13 CX = 12, by the second theorem.
Example 2Circle O has a radius of 13 inches. Radius OB is
perpendicular to chord CD, which is 24 inches long.
Compute length of segment OX.
Draw segment CO, CO = 13 CX = 12, by the second theorem.
Example 3
Example 3
Example 3
Example 3
Example 3
Example 3
Example 3
Example 3
Example 3
CW 2, HW
