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In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. B. C. AB CD IFF AB = DC. A. D. 12 in. 120. 120. x. x = 12 in. x + 40. 2x + 10. 2x + 10= x + 40 x = 30. - PowerPoint PPT Presentation
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A
B
C
D
In the same circle, or in congruent circles, two minor arcs are congruent
if and only if their corresponding chords are congruent.
AB CD IFF AB = DC
120 120
12 in.
x
x = 12 in.
2x + 10 x + 40
2x + 10= x + 40
x = 30
A
B
C
D
What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB?
It’s the DIAMETER!!!
Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
y4
x
60x = 4
y = 30
Example 2EX 2: In P, if PM AT, PT = 10, and PM = 8, find AT.
T
AM
P
MT = 6AT = 12
Example 3In R, XY = 30, RX = 17, and RZ XY.
Find RZ.
R
X
Z
Y
RZ = 8
Example 4 IN Q, KL LZ. IF CK = 2X + 3 and CZ = 4x, find x.
K
Q
C
L
Zx = 1.5
In the same circle or in congruent circles, two chords are congruent if
and only if they are equidistant from the center.
A
B
C
D
M
L
P
AD BC
IFF
LP PM
Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x.
P
R
Q
A
x = 32
Ex. 6: IN K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find x.
Y
T
S
K
x = 8
U
R
E