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 the radius is perpendicular to the tangent at the point of contact. 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
= $\frac{1}{2}\times circumference=\frac{1}{2}\times 14cm=7cm$