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Please help. 40 points! Geometry circles

Please help. 40 points! Geometry circles-example-1
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1 Answer

3 votes

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

-----------------------------------------------------------------------------

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

------------------------------------------------------------------------------

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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User Haysclark
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