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A circle with centre (X, Y) and radius r has formula:

(x - X)Â² + (y - Y)Â² = rÂ²

As the points (6, 3), (-5, 2) and (7, 2) are on the circle:

- (6 - X)Â² + (3 - Y)Â² = rÂ²
- (-5 - X)Â² + (2 - Y)Â² = rÂ²
- (7 - X)Â² + (2 - Y)Â² = rÂ²

Subtracting (2) from (3) gives:

(7 - X)Â² - (-5 - X)Â² + (2 - Y)Â² - (2 - Y)Â² = rÂ² - rÂ²

â†’ 49 - 14X + XÂ² - (25 +10X +XÂ²) = 0

â†’ 49 - 25 -14X -10X +XÂ² - XÂ² = 0

â†’ 24 - 24X = 0

â†’ 24X = 24

â†’ X = 1

Substituting this into (1) and (2) gives:

- (6 - 1)Â²+ (3 - Y)Â² = rÂ² â†’ 5Â² + 9 - 6Y + YÂ² = rÂ² â†’ 34 - 6Y + YÂ² = rÂ²
- (-5 - 1)Â² + (2 - Y)Â² = rÂ² â†’ (-6)Â² + 4 - 4Y + YÂ² = rÂ² â†’ 40 - 4Y +YÂ² = rÂ²

Subtracting (1) from (2) now gives:

40 - 34 - 4Y - (-6Y) +YÂ² - YÂ² = rÂ² - rÂ²

â†’ 6 + 2Y = 0

â† 2Y = -6

â†’ Y = -3

â†’ The equation of the circle is (x - 1)Â² + (y - -3)Â² = rÂ² â†’ (x - 1)Â² + (y + 3)Â² = rÂ²

Using one of the points (6, 3), say, and substituting for x and y gives:

(6 - 1)Â² + (3 + 3)Â² = rÂ²

â†’ 5Â² + 6Â² = rÂ²

â†’ 25 + 36 = rÂ²

â†’ rÂ² = 61

The area of a circle is given by area = Ï€ Ã— radiusÂ²

â†’ the area of the circle through those three points is Ï€ Ã— 61 = 61Ï€ unitsÂ² â‰ˆ 191.64 unitsÂ²

Q: What is the area of a circle whose circumference passes through the points of 6 3 and -5 2 and 7 2 on the Cartesian plane showing work?

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The diameter of a circle is the length of a line passing through the center of a circle that connects two points on the circumference. The circumference is the distance around the edge of a circle.

A chord is a straight line that spans the circumference of a circle and the diameter of a circle is a straight line in a circle spanning its circumference and passing through the circle's centre.

Points: (0, 0) and (3, 4) Using Pythagoras: distance fro (0, 0) to (3, 4) = 5 cm which is the radius Circumference: 2*pi*5 = 31.416 cm rounded to three decimal places Area: pi*5^2 = 78.540 square cm rounded to three decimal places

Circumference is the perimeter of a circle Diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle

It works out that the centre of the circle is at (4, -3) on the Cartesian plane and its area is 56.549 square cm rounded up to three decimal places.

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It has centre (0, 0) and radius 5.

In the case of a circle: Diameter: The distance through the circle - from one end to the other, passing through the center. Circumference: The distance around the circle.

The diameter of a circle is the length of a line passing through the center of a circle that connects two points on the circumference. The circumference is the distance around the edge of a circle.

The diameter of a circle is a straight line going from one point on the circumference (the boundary) of the circle, through the centre of the circle, to another point on the circumference.

A chord is a straight line that spans the circumference of a circle and the diameter of a circle is a straight line in a circle spanning its circumference and passing through the circle's centre.

Points: (0, 0) and (3, 4) Using Pythagoras: distance fro (0, 0) to (3, 4) = 5 cm which is the radius Circumference: 2*pi*5 = 31.416 cm rounded to three decimal places Area: pi*5^2 = 78.540 square cm rounded to three decimal places

Circumference is the perimeter of a circle Diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle

360 degrees * * * * * That is a nonsensical answer. The diameter of a circle is a straight line segment, going from the circumference of the circle, through the centre, to the circumference on the other side.

Diameter is the length of a straight line passing through the center of a circle or sphere and connecting two points on the circumference of the circle or the surface of the sphere. Circumference is the length of the closed curve of a circle.

It works out that the centre of the circle is at (4, -3) on the Cartesian plane and its area is 56.549 square cm rounded up to three decimal places.

It works out that the circle's centre is at (3, -2) and its radius is 5 on the Cartesian plane.

the diameter oh whoops i thought the circumference was it... the circumference is the length around the circle