Question

Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25$\pi$ ${cm}^2$, then the distance between the lines is

• A. 5 cm
• B. 8 cm
• C. 10 cm
• D. 25 cm

Answer 1

The correct option is C

10 cm

Given that the area of circle = $25\pi c{m}^2$​
$⟹\pi r^2=25\pi$, where $r$ is the radius of the circle.
$i.e.,r^2=25⟹r=\pm 5$
Since radius is a non-negative quantity, we have $r=5cm$

Now, the distance between the two parallel lines
= Diameter of the circle
= $2\times$ Radius of the circle = 10 cm.