SOLUTION: What is the circumference of a circle with center A(2,3) and passes through B(4,5)?

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Question 955158: What is the circumference of a circle with center A(2,3) and passes through B(4,5)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the circumference of a circle is C=2r%2Api
a circle with center A(2,3) and passes through B(4,5) will have a radius r equal to distance between points A and B
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (2, 3), we can say (x1, y1) = (2, 3)
So x%5B1%5D+=+2, y%5B1%5D+=+3


Since the second point is (4, 5), we can also say (x2, y2) = (4, 5)
So x%5B2%5D+=+4, y%5B2%5D+=+5


Put this all together to get: x%5B1%5D+=+2, y%5B1%5D+=+3, x%5B2%5D+=+4, and y%5B2%5D+=+5

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Now use the distance formula to find the distance between the two points (2, 3) and (4, 5)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%282+-+4%29%5E2+%2B+%283+-+5%29%5E2%29 Plug in x%5B1%5D+=+2, y%5B1%5D+=+3, x%5B2%5D+=+4, and y%5B2%5D+=+5


d+=+sqrt%28%28-2%29%5E2+%2B+%28-2%29%5E2%29


d+=+sqrt%284+%2B+4%29


d+=+sqrt%288%29


d+=+sqrt%284%2A2%29


d+=+sqrt%284%29%2Asqrt%282%29


d+=+2%2Asqrt%282%29


d+=+2.82842712474619

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Answer:


The distance between the two points (2, 3) and (4, 5) is exactly 2%2Asqrt%282%29 units


The approximate distance between the two points is about 2.82842712474619 units



So again,


Exact Distance: 2%2Asqrt%282%29 units


Approximate Distance: 2.82842712474619 units




so, if we use the d=2sqrt%282%29, then C=2r%2Api will be
C=2%2A2sqrt%282%29%2Api
C=4sqrt%282%29%2Api or as decimal
C=4%2A2.83%2A3.14
C=35.5448
C=35.51