The circle c has centre (2, –3) and a radius of 4 cm - Leaving Cert Mathematics - Question 3 - 2016

To draw the circle, first locate the center at (2, -3) on the grid.

Using a compass or free-hand, draw a circle with a radius of 4 units, ensuring that the points on the circumference maintain equal distance from the center.

The circle should pass through the points (2, 1), (2, -7), (6, -3), and (-2, -3). Make sure to label the center clearly.

To verify if the point (3, 1) is outside the circle, substitute the coordinates into the circle's equation:

$(3 - 2)^2 + (1 + 3)^2 \n = 1^2 + 4^2 \n = 1 + 16 = 17\n$

Since $17 > 16$, the distance from the center to the point (3, 1) is greater than the radius of the circle. Thus, the point (3, 1) is indeed outside the circle c.

The smallest four-sided figure that can encompass the circle is a square.

The diameter of circle c is given by:

$d = 2r = 2 \times 4 = 8 \text{ cm}$

Thus, the dimensions of the square will be 8 cm x 8 cm.

The area A of this square is calculated as:

$A = ext{side}^2 = 8 \times 8 = 64 \text{ cm}^2$

Therefore, the area of the smallest four-sided figure that will fit around circle c is 64 cm².