What does it mean to 'inscribe' a figure?

To inscribe a figure means to draw a figure within another such that the boundaries of the inscribed figure touch the boundaries of the outer figure at specific points without intersecting them. This concept is commonly used in geometry, where a circle can be inscribed within a polygon. For instance, when a circle is inscribed in a triangle, it touches each side of the triangle at exactly one point, highlighting the relationship between the two figures. This precision in contact is essential to the definition of inscribing, as it distinguishes the process from simply overlapping or dividing figures, where such boundary interactions would not necessarily be maintained.