The point (1,4) lies on a circle that is centered at (1, 1). Which statements are correct?
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.

Step-by-step explanation:

Let's get to the answer using the formula for EQUATION OF A LINE at the center of a circle.

The equation is expressed as:

(x - h) ^2 +. (y - k) ^ 2 = r ^2

Where:

(h, k) = The center of the circle

(x, y) = Some points around the circle

(r) = Radius of the circle

Let's apply the formula to solve the question:

(x - h) ^2 +. (y - k) ^ 2 = r ^2

(1 - 1)^2 + (4 - 1)^2 = r^2

0^2 + 3^2 = r^2

0 + 9 = r^2

r^2 = 9

r = √9

r = 3

Therefore,

The circle's radius is 3 units.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

2/3

step-by-step explanation: