Question

question 25 of 25 if a circle is inscribed in a square, which of the following must be true? check all that apply. a. the square is circumscribed about the circle. b. each vertex of the square lies outside the circle. c. the circle is congruent to the square. d. the circle is tangent to each side of the square. e. each vertex of the square lies inside the circle.

Explanation:

• Option A: When a circle is inscribed in a square, the square is circumscribed about the circle (the square encloses the circle with the circle touching the square's sides), so this is true.
• Option B: The vertices of the square are at a distance equal to half the diagonal of the square from the center, while the radius of the circle is half the side length of the square. Since the diagonal of the square is longer than the side length, the vertices lie outside the circle, so this is true.
• Option C: A circle and a square are different shapes and cannot be congruent (congruent figures must have the same shape and size), so this is false.
• Option D: By definition, an inscribed circle (incircle) of a square is tangent to each side of the square, so this is true.
• Option E: As explained in Option B, the vertices are outside the circle, not inside, so this is false.

Answer:

A. The square is circumscribed about the circle.
B. Each vertex of the square lies outside the circle.
D. The circle is tangent to each side of the square.