How do I find the radius when given a point and center of a circle??

Question

Center: (3,1)
Point (4,2)

Help me, I really have no clue how to find the radius

Answer 1

You'll need to use the distance formual to find the length of the radius.

sqrt((x2 - x1)^2 + (y2 - y1)^2) = distance

center(3,1), point (4,2)
sqrt((4 - 3)^2 + (2 - 1)^2)
sqrt((1)^2 + (1)^2)
sqrt (1 + 1)
sqrt(2)

Depending on what type of answer is required it's either the square root of two or the decimal aproximation: 1.4142.....

Answer 2

Your equations is related very closely to the center. You need a point so you can find the distance. For example:
The distance from (3,1) to (4,2) uses the Pythagorean theorem
a^2+b^2=c^2
a=4-3=1
b=2-1=1
1^2+1^2=2
This gives you the rest of your equation
(x-3)^2+(y-1)^2=2

The formula is (x1-x2)^2+(y1-y2)^2=r^2

I hope this helps

Answer 3

The point is somewhere on the circle and the Center is in the middle of the circle.
Find the distance between the two and you will have the length of any radius because all of them are the same length.

take the difference between the first coordinate of the point and the first coordinate of the Center and let that be called dX.

take the difference between the second coordinate of the point and the second coordinate of the Center and let that be called dY.

multiply dX times itself to get dX^2

Multiply dY times itself to get dY^2

Add the last two results together to get (dX^2 + dY^2)

Take the square root and the result will be the distance between the center and the point on the circle.

This method is based on the Pythagorean theorem.