Warm - up
(x – h)2 + (y – k)2 = r2
Give the equation in the circle in standard form.
1. Center (5,6) radius:4
2. Center ( 3, - 4) radius:3
Find the center and radius of the circle:
3. (x – 2)2 + (y – 7)2 = 9
4. (x
5.
+ 6)2 + (y – 3)2 = 7
Give the radius of the circle if the center of the circle is
(4, 6) and a point on the circle is (5, - 2).
Central Angles and Arcs
Sec: 10.6
Sol: G.11b,c
Central angles:
A central angle is an angles whose vertex is
the center of the circle.
C
∠APC, ∠CPB and ∠APB
Are central angles.
B
A
P
Key concept: The sum of the measure of
the central angles in a circle is 360°.
m∠1+m∠2+m∠3 = 360°
ARC: Is a part of a circle
THREE TYPES OF CIRCLEs :
A) SEMI – CIRCLE (Half a circle) = 180°
R
T
P
S
TRS is a semi-circle
mTRS is 180°
B) MINOR ARC: shorter than a semi-circle
60°
S
R
60°
P
RS is a minor arc
mRS = m∠RPS
Note: The Measure of a minor arc = the measure of its
central angle.
C) Major Arc: Larger than a semi-circle.
RTS is a major arc
mRTS = 360 – mRS
S
R
P
T
Note: The measure of a major arc is:
360 – the measure of its related minor
arc.
In the same or in congruent circles, two
arcs are congruent iff their corresponding
central angles are congruent.
Adjacent Arcs: two arcs in the same circle that have
exactly one point in common.
Note: you can add the measures of adjacent arc just like
you add the measures of adjacent angles.
Arc Addition Postulate:
mABC = mAB + mBC
C
B
P
A
Ex: Find the measure of each arc
58°
D
A) BC
C
B) BD
B
32°
C) ABC
O
D) AB
A
E) BAD
ARC LENGTH:
Another way to measure an arc is by its length. Since
an arch is a part of a circle, its length is PART of the
circumference.
Ex: Find the length of XY. Leave your answer in term of π.
X
16 in
Y
Ex: Find the length of XPY. Leave your answer in
terms of π. XPY = 240° with a radius of 6
X
O
Y
P
Ex: Find the length of a semi – circle in circle P
with a radius of 1.3 m.
P
Suggested assignments:
Classwork: WB pg 271-272 1-3, 4-40 even
Homework: Pg 654 9-11, 24, 26, 29, 30-34,
48