The point (1, 4) lies on a circle that is centered at (1, 1). which statements are correct? check all that apply. the circle’s radius is 2 units. the circle’s radius is 3 units. the circle’s radius is 9 units. the point (–2, 1) lies on the circle. the point (3, 3) lies on the circle.

the circle's radius is 3 units

the point (- 2, 1 ) lies on the circle

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b) are the coordinates of the centre and r is the radius

the radius is the distance from the centre to the point (1, 4 ) on the circle

using (1, 4) and (1,1) in the distance formula, then

r = √(1 - 1 )² + (1 - 4)² = √(0 + 9) =√9 = 3 ⇒ r² = 9

(x - 1 )² + (y - 1 )² = 9 ← equation of circle

substitute the given points into the equation and if equation is true then they lie on the circle

(- 2, 1 ) : (- 2 - 1 )² + (1 - 1 )² = 9 + 0 = 9 ← true

Hence (- 2, 1 ) lies on the circle

(3, 3 ) : (3 - 1 )² + (3 - 1 )² = 4 + 4 = 8 ≠ 9

(3, 3 ) does not lie on the circle

117°

same side interior angles theorem