The document discusses key concepts in geometry related to circles: - A central angle is an angle with its vertex at the center of a circle, and its arms formed by two radii. The central angle is subtended by both the chord and arc connecting the same two points on the circle. - An inscribed angle is an angle with its vertex on the circle, and its arms formed by two chords. The inscribed angle is subtended by both the chord and arc connecting the same two points. - Important theorems about angles in circles include: an angle inscribed in a semicircle is a right angle, the measure of a central angle is equal to twice the measure of the inscribed

3. Minor Arc the smaller arc
.
C
.
A
.
O
.
Major Arc
B
the larger arc

4. .
C
Central Angle:
.
an angle that has it's vertex
at the centre, two radii form A
the arms of the angle.
.
O
Central angle AOC is
subtended by the chord AC
.
and by the arc AC.
B

5. .
C
Inscribed angle:
.
an angle that has it's vertex on
the circle, and two chords A
form the arms.
.
O
Inscribed angle ABC is
.
subtended by the chord AC, and
by the arc AC.
B

8. Angles in a Circle Theorem
­ The angle inscribed in a semicircle is a right angle
­ The measure of the central angle is equal to twice
the measure of the inscribed angle subtended by
the same arc.
­ Inscribed angles subtended by the same arc, or
by equal arcs, are congruent.

9. Find the measure of angles
a, and angle b.
a
.
O o
b 50

10. Find the measures of angles
x, y, and z.
o
40
y
o
55
x
z
o
25

11. Exercise 31
Questions 1 ­ 7