Question

Which of the following is/are true for a circle?

• A. Diameter of a circle is twice the radius of the circle.
• B. A circle is defined as the collection of all points that are equidistant from a fixed point(centre).
• C. Radius of a circle is twice the diameter of the circle.
• D. Circumference of a circle is $2\pi r$, where $r$ is the radius of circle.

Answer 1

Answer: (A), (B), (D)

Circumference of a circle is $2\pi r$, where $r$ is the radius of circle.

Lets draw a circle of radius r and diameter d.
Properties of a circle:
$1$. A circle is defined as the collection of all points that are equidistant from a fixed point(centre).

$2.$ Diameter of a circle is twice the radius of the circle.
$d=2r\Rightarrow r=\frac{d}{2}$
Radius of a circle is half of diameter of the circle.
$\therefore$Option (c) is incorrect.

$3.$Circumference of a circle is $2\pi r$, where $r$ is the radius of circle.