1)
As the circle are congruent with given chords so
y = 2x-3 and y=x-1
, we can use the substitution method , So substitute y = 2x-3 , in the second equation
we get
2x-3 = x-1
subtract x from both sides
x -3 = -1
add 3 to both sides
x= 2
y = 2(2)-3 = 1
y=1
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2) we equate the chord lengths
So
x+5 = 2x-10
subtract x from both sides
5 = x-10
add 10 to both sides
15 = x
x=15
Length of QR = x+5 = 15+5 = 20
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3)Again we equate the chord lengths as they are congruent
4x+2 = x+7
subtract x from both sides
3x+2 = 7
subtract 2 from both sides
3x=5
Divide both sides by 3
x=5/3
Length of QR = 4x+2 = 4(5/3) +2 = 20/3 +2 = 26/3
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4) again we equate the sides which are congruent
y=x+2 and y=2x-1
Substituting we get
x+2 = 2x-1
Subtract x from both sides
2= x-1
Add 1 to both sides
3=x
x=3
and y = x+2 = 3+2 = 5
y=5
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