2. Circle is the set of all points that are of the same
distance from a given point in a plane.
Center or the central point is the given point of
the circle.
Radius is the line segment from the center to any
point on the circle.
O
B
3. Diameter is a chord that passes through the center of the
circle.
B
c
Chord a line segment whose endpoints both
lie on the circle.
4. O
C
B
A
Interior of the circle is the set of points in the plane of a circle
whose distances from the center are less than the length of
the radius.
D
G
F
E
Exterior of the circle is set of points in the plane of a
circle whose distances from the center are greater
than the length of the radius.
5. D
Points E, F, and G are in the interior of
the circle.
Points H, I, J are in the exterior of the
circle.
6. The following theorems shows the relationship between the
radii and chords of circles.
Theorem
If a radius is perpendicular to a chord, then it bisects the chord.
7.
8. Example FIND AD, CD, AC
SOLUTION
AD = CD
3X + 2 = 5X - 4
2 + 4= 5x-3x
6 = 2X
6
2
=
2𝑋
2
3 = X
Hence:
AD = 3x +2
= 3( 3) + 2
= 9 + 2
AD = 11
CD = 5x -4
= 5(3) - 4
= 15 -4
CD=11
AC = AD + CD
= 11 + 11
= 22
9. Theorem
If a radius of a circle bisects a chord that is not a diameter, then it is
perpendicular to the chord.
10. Theorem
The perpendicular bisector of a chord passes through the center of
the circle.
PQ passes through O
Midpoint is the middle point of a line
segment.
16. 1. If AG = 24 cm, what is AC?
2. If AC = 38 cm, what is CG?
3. If OG = 5cm and OC=13cm,
what is GB?
4. If CG = 42cm, what is AC?
5. If AO = 96 cm, what is AE?
48cm
19cm
8cm
84cm
192cm
