Rajesh is 29 m away from the centre of a circular flower bed. Find the distance he has to cover to reach the flower bed along the tangential path if the radius of the flower bed is 20m.

Let the centre of circular flower bed be O and radius OB = 20 m

Let Rajesh is at point A, and he has to travel tangential path to reach flower bed which is AB as shown

Now we know that radius is perpendicular to point of contact

Hence OB is perpendicular to AB

Hence ∠ABO = 90°

Consider ΔABO

Using Pythagoras theorem

⇒ AB² + OB² = AO²

⇒ AB² + 20² = 29²

⇒ AB² = 29² - 20²

Using a² – b² = (a + b)(a – b)

⇒ AB² = (29 – 20)(29 + 20)

⇒ AB² = 9 × 49

⇒ AB = √(9 × 49)

⇒ AB = ± (3 × 7)

⇒ AB = ±21

As length cannot be negative

⇒ AB = 21 m

Hence Rajesh has to cover 21 m to reach the flower bed along the tangential path.