lesson 11.2 chords and arcs
DESCRIPTION
LESSON 11.2 CHORDS AND ARCS. OBJECTIVE: To use chords, arcs and central angles to solve problems To recognize properties of lines through the center of a circle. Label each picture as a chord, arc or a central angle:. x . central angle. arc. chord. Theorem 11.4. - PowerPoint PPT PresentationTRANSCRIPT
LESSON 11.2 CHORDS AND ARCS
OBJECTIVE: To use chords, arcs and central angles to solve problems
To recognize properties of lines through the center of a circle
Label each picture as a chord, arc or a central angle:
x
arc chordcentral angle
Theorem 11.4
Within one circle or within (two or more) congruent circles:
arcs have central angles
central angles have chords
chords have arcs
(1)
(2)
(3)
IFS AND THENS
Example #1: In the diagram, circle O circle D. Given that BC PF, what can you conclude? And why (theorem)?
O D
AND
BC PF
C
B
O
P
D F
Theorem:
arcs have ’s
Theorem:
’s have chords
they are equidistant from the center.
they are .center of a circle, then
Theorem 11.5
Within one circle or within (2 or more congruent circles): (Biconditional)
If chords are equidistant from the(1)
(2) If two or more chords are , then
C
AB
DE
F
G
IF THEN AB CD
AB CD EG FG
EG FG
IF THEN
Ex. #2 Find a. Give reason (theorem).
Therefore, a =
So, they are
If chords are equidistant from the center of the Circle, then they are .
25 un.
THEOREM
a and PR are equidistant from center.
Theorem 11.6In a circle, if a diameter is perpendicular to a chord, then it
bisects the chord and its arcs.
IF THEN
Theorem 11.7
In a circle, if a diameter bisects a chord (that is not another diameter) then it is
perpendicular to the chord.
IF THEN
Theorem 11.8
In a circle, if a segment is the perpendicular bisector of a chord, then
it contains the center of a circle
IF
A
B
THEN
AB passes through the center of the circle.
A
B
Ex. #3 Find r. State the reason (theorem).
If KN were extended, itwould be a diameter and it is to LM.
Therefore,
r2 = 72 + 32 r2 = 49 + 9 r2 = 58 r = 58
If a diameter is to a chord then it bisectsthe chord.
it bisects LM.So, LN = 7. Why?
Ex. #4 Find y. State the reason (theorem)
Is this a right triangle?
Yes.
152 = y2 + 112 225 = y2 + 121 104 = y2
2 26 = y
If a diameter bisects a chord then it is to the chord.
Why?
ASSIGNMENT: Page 593 #1 – 16
Write out the theorem used for #3-16