Which is true about the relationship between circle o and square RSTU? select all they apply.
A the circumference of circle o is equal to the perimeter of square RSTU
B square RSTU is inscribed in circle o
C circle o is inscribed in square RSTU
D segment or is a radius of circle o
E the area of square RSTU is greater than the area of circle o
F the diameter of circle o is equal to the side length of square RSTU
To answer this question, we need to analyze the properties of circles and squares.
A) The circumference of a circle is given by the formula C = 2πr, where r is the radius. The perimeter of a square is calculated by adding up the lengths of all four sides. If we assume that the side length of the square is equal to the radius of the circle, then the circumference of the circle (2πr) will indeed be equal to the perimeter of the square.
B) If a square is inscribed in a circle, it means that all four vertices of the square lie on the circumference of the circle. In this case, the answer would be "yes" as it indicates that square RSTU is inscribed in circle O.
C) If a circle is inscribed in a square, it means that the circumference of the circle is tangent to all four sides of the square. Given the information provided, we cannot determine if circle O is inscribed in square RSTU, so the answer would be "uncertain."
D) A radius is a line segment that connects the center of a circle to any point on its circumference. If segment OR is a radius of circle O, then it would be true.
E) Comparing the area of a square and the area of a circle, we know that the area of a circle is given by the formula A = πr^2, while the area of a square is calculated by squaring the length of its side (A = s^2). Without knowing the values of the radius of the circle and the side length of the square, we cannot determine if the area of square RSTU is greater than the area of circle O, so the answer would be "uncertain."
F) The diameter of a circle is a straight line that passes through the center, and its length is twice the radius. If the diameter of circle O is equal to the side length of square RSTU, then it would be true.
Based on the information provided, the correct options would be:
A) True
B) True (assuming the vertices of the square lie on the circumference of the circle)
D) True
F) True