Question

Which one of the following is a true statement about a circle inscribed in a regular polygon?

A. The sides of the polygon are chords of the circle.
B. The sides of the polygon are tangents of the circle.
C. The vertices of the polygon are on the circumference of the circle.
D. The area of the circle is equal to the area of the polygon.

Answer 1

Given, a circle inscribed in a regular polygon.

From the given different statements,

A. The sides of the polygon are chords of the circle.

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

C. The vertices of the polygon are on the circumference of the circle.

D. The area of the circle is equal to the area of the polygon.

Since, the Circle is inscribed inside the regular polygon, the sides of the polygon must be touching the circle. When we have such an arrangement then those sides must be tangent to the circle. So the sides of the polygon must be a tangent.

Hence, the sides of the polygon are tangents to the circle.

Option B is true and others are false

Answer 2

I think that B is correct

Answer 3

Given, a circle inscribed in a regular polygon.

From the given different statements,

A. The sides of the polygon are chords of the circle.

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

C. The vertices of the polygon are on the circumference of the circle.

D. The area of the circle is equal to the area of the polygon.

Since, the Circle is inscribed inside the regular polygon, the sides of the polygon must be touching the circle. When we have such an arrangement then those sides must be tangent to the circle. So the sides of the polygon must be a tangent.

Hence, the sides of the polygon are tangents to the circle.

Option B is true and others are false