Question

Consider a point A on the circle of radius $\frac{7}{\pi }$ cm as shown in the figure. A ball on point A moves along the circumference until it reaches a point B. The tangent at B is parallel to the tangent at A. What is the distance traveled by the ball? (Consider the ball to be a point object)

Note: The point B in the diagram may not represent its actual position.

• A. 3.5cm
• B. 7 cm
• C. 14cm
• D. 28 cm

Answer 1

The correct option is B 7 cm

Given that the tangent at point B is parallel to the tangent at point A. The points A and B would be as follows


The tangents at A and B are parallel, so the radii through A and B should be parallel to each other, since radius is perpendicular to the circle. Since the radius passes through the centre of the circle, the radii through A and B must lie on the same straight line. The line AB will be the diameter of the circle.
Now A and B are on two ends of the diameter of the circle. The distance travelled along the circle from A to B will be half the circumference of the circle.
Now, Circumference = $2\pi r=2\times \pi \times \frac{7}{\pi }=14cm$
$Distance=\frac{1}{2}\times circumference=\frac{1}{2}\times 14cm=7cm$