Question

Two points are randomly chosen on the circumference of a circle of radius $r$. The probability that the distance between the two points is at least $r$ is equal to

• A. $\frac{2}{\pi }$
• B. $\sin r$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (D)

Two point on a circumference of circle of radius $r$
Distance between two points is atleast $r$
$\therefore$ Angle subtends to chord of length
atleast $r$ is greater than or equal to $60^{\circ }$

$\therefore$ Required pronabaility $=1-\frac{60}{180}$
$=1-\frac{1}{3}=\frac{2}{3}$