parts of a circle

1. Activity 1: 4 Pics – One Word

2. Which of the following are good
physical models of a circle?

3. LEARNING OBJECTIVES
a.Identify the chords, arcs, central angles
and inscribed angles of a circle.
b.Name the chords, arcs, central angles,
and inscribed angles of a circle.
c.Value accumulated knowledge as means
of new understanding.

4. CIRCLES

5. CIRCLE
• A closed curve figure, all points
of which are equidistant from a
fixed point called vertex.

7. Parts of a circle

8. RADIUS
• A segment whose endpoints are in the
center of the circle and the other
endpoint is on the circle.

9. Chord
• Is a segment whose endpoints
are any two points on the circle.

10. Diameter
• A chord which passes through
the center of a circle.

11. Secant
• Line that intersects the circle at two
points

12. Tangent
• Is a line in the plane of a circle
that intersects the circle at
exactly one point. This point is
called the point of tangency.

13. Central Angle
• An angle formed by two radii of
a circle with vertex on the
center of the circle.

14. INSCRIBED ANGLE
• An angle whose vertex is on a circle
and whose sides contain chords of the
circle. The arc that lies in the interior of
an inscribed angle and has endpoints
on the angle is called the intercepted
arc of the angle.

15. Arc
• A part or a portion of a circle.

16. Semi - circle
• Half of a circle, it measures
180°.

17. Minor Arc
• Less than half of a circle

18. Major Arc
• More than half a circle.

19. ACTIVITY 2:Use ʘP below to identify and
name the following:
1. 2 radii
2. a diameter
3. 2 chords
4. 2 semicircles
5. 2 minor arcs
6. 2 major arcs
7. 2 central angles
8. 2 inscribed angles

20. Activity 3: Make a circle and Name it
as ʘC. Create the different parts of a
circle and LABEL its part.
1. radius
2. diameter
3. chord
4. semicircle
5. minor arc
6. major arc
7. central angle
8. inscribed angle

21. Generalization:
What are the different parts of a circle?
Describe each part.

22. Evaluation:Use ʘ O below to identify and name the
following:
1. radius
2. diameter
3. chord
4. semicircle
5. minor arcs
6. major arcs
7. central angles
8. inscribed angles

24. Congruent Circles and
Congruent Arcs
• Congruent circles
are circles with congruent radii.

25. Congruent
arcs
• are arcs of the same circle or of congruent
circles with equal measures.

26. Theorems on Central Angles,
Arcs, and Chords
1. In a circle or in congruent circles, two minor
arcs are congruent if and only if their
corresponding central angles are congruent.

27. 2. In a circle or in congruent circles, two
minor arcs are congruent if and only if their
corresponding chords are congruent.

28. 3. In a circle, a diameter bisects a chord and an
arc with the same endpoints if and only if it is
perpendicular to the chord.

29. Arc Addition Postulate
The measure of an arc formed by two
adjacent arcs is the sum of the
measures of the two arcs.
adjacent arcs are arcs with exactly one
point in common.

30. 71 + 84 = 155

31. Sector and Segment of a
Circle
Sector of a circle
• is the region bounded
by an arc of the circle
and the two radii to
the endpoints of the
arc.

32. Area of a Sector of a
Circle
Area of Sector =( )( )
Measure of the Arc
360
Area of
the ʘ
𝐴 = 𝜋𝑟2

33. segment of
a circle
• is the region
bounded by an arc
and the segment
joining its
endpoints.

34. Segment of a circle= Area of a sector – Area of the Triangle
If m PQ = 90°
and the radius is
5 cm.

35. Arc
Length
Where :
A=degree measure of the arc
r = radius of the circle
l = the arc length
360 = degree measure of the whole circle
2𝜋r = the circumference

36. • Example: An arc of a circle measures
45°. If the radius of the circle is 6 cm,
what is the length of the arc?