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. each vertex of the square lies inside the circle. b. the circle is tangent to each side of the square. c. each vertex of the square lies outside the circle. d. the circle is congruent to the square. e. the square is circumscribed about the circle.

Explanation:

Step1: Understand inscribed - circle meaning

When a circle is inscribed in a square, the circle touches each side of the square at exactly one point. This means the circle is tangent to each side of the square (B is true).

Step2: Analyze vertex - circle position

The radius of the inscribed circle is less than half of the diagonal of the square. So, each vertex of the square lies outside the circle (C is true).

Step3: Define circumscribed - square

If a circle is inscribed in a square, then the square is circumscribed about the circle. That is, the square surrounds the circle and the circle is tangent to the sides of the square (E is true).

Step4: Analyze incorrect options

A is false because vertices are outside not inside. D is false because a circle and a square cannot be congruent as they are different - shaped figures.

Answer:

B. The circle is tangent to each side of the square., C. Each vertex of the square lies outside the circle., E. The square is circumscribed about the circle.