Question

which one of the following is a true statement about a circle inscribed in a regular polygon?
a) the area of the circle is equal to the area of the polygon.
b) the vertices of the polygon are on the circumference of the circle.
c) the sides of the polygon are chords of the circle.
d) the sides of the polygon are tangents of the circle.

Explanation:

• Option A: A circle inscribed in a regular polygon has a smaller area than the polygon.
• Option B: Vertices of a polygon are on the circumference of a circumscribed circle, not an inscribed one.
• Option C: Chords are line - segments with endpoints on the circle. Sides of an inscribed - circle - related polygon are tangents, not chords.
• Option D: By the definition of an inscribed circle in a polygon, the sides of the polygon are tangent to the circle.

Answer:

D. The sides of the polygon are tangents of the circle.