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Identify these statements as "Always, Sometimes, or Never"A circle can be inscribed in any regular polygon.A circle can be inscribed in an isosceles trapezoid.If a line segment is drawn from the center of any regular polygon to any of its vertices, the segment is a radius of the inscribed circle.A circle can be circumscribed about an equilateral triangle.Any triangle, regular or not, can be inscribed in a circle.If two circles are concentric, then their radii are congruent.If a circle is inscribed in a square, then the diagonal of the square contains a diameter of the circle.If a regular polygon is inscribed in a circle, then all diagonals of the polygon pass through the center of the circle.Circles can be inscribed inside of quadrilaterals.A parallelogram can be inscribed inside of a circle.

Question

Identify these statements as "Always, Sometimes, or Never"A circle can be inscribed in any regular polygon.A circle can be inscribed in an isosceles trapezoid.If a line segment is drawn from the center of any regular polygon to any of its vertices, the segment is a radius of the inscribed circle.A circle can be circumscribed about an equilateral triangle.Any triangle, regular or not, can be inscribed in a circle.If two circles are concentric, then their radii are congruent.If a circle is inscribed in a square, then the diagonal of the square contains a diameter of the circle.If a regular polygon is inscribed in a circle, then all diagonals of the polygon pass through the center of the circle.Circles can be inscribed inside of quadrilaterals.A parallelogram can be inscribed inside of a circle.

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Solution

  1. Always: A circle can be inscribed in any regular polygon.
  2. Sometimes: A circle can be inscribed in an isosceles trapezoid.
  3. Always: If a line segment is drawn from the center of any regular polygon to any of its vertices, the segment is a radius of the inscribed circle.
  4. Always: A circle can be circumscribed about an equilateral triangle.
  5. Always: Any triangle, regular or not, can be inscribed in a circle.
  6. Never: If two circles are concentric, then their radii are congruent.
  7. Always: If a circle is inscribed in a square, then the diagonal of the square contains a diameter of the circle.
  8. Never: If a regular polygon is inscribed in a circle, then all diagonals of the polygon pass through the center of the circle.
  9. Always: Circles can be inscribed inside of quadrilaterals.
  10. Sometimes: A parallelogram can be inscribed inside of a circle.

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