What is the approximate circumference if the circle that has a center at (2,1) ans passes through the point (2,5). 1. 8 units 2. 13 units 3. 25 units 4. 50 units

We have: center(2,1) and a point on the circle (2,5):
r=5-1=4
circumference of a circle: \( 2*\pi*r=2*3,14*4=25,12 \)
Answer 3: 25

First we can find the radius of the circle by applying the distance formula to the circles center and a point on the circle ( √((x-h)^2 + (y-k)^2)=distance between the points, where (h, k) is the center and (x, y) is the point). Since the center is (2,1) and a point on the circle is (2,5) we can plug them in to get √((2-2)^2 + (5-1)^2)  -> √(0^2 + 4^2) -> √(0+16) -> 4. Now we know the radius is 4, so to find the diameter we need to multiply the radius by 2 which gives us 8. Now we use the formula for circumference to find the circumference, diameter*π -> 8π ≈ 25
So your answer is #3. 25 units


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