Please submit your concern

Question:

Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a, b and c, respectively. Which of the following is true?

Explanation:

The radius of each circular park = r

A₁B₁ = A₁E = r

Distance travelled by A = a = 3 × 2r = 6r

∆A₁B₁D is a right angle triangle with ∠A₁B₁D = 30° and ∠B₁A₁D = 60°

∴ B₁D = $\frac{\sqrt{3}r}{2}$

∴B₁B₂ = 2r + 2 × $\frac{r\sqrt{3}}{2}=r(2+\sqrt{3})$

∴ Distance travelled by B = b = 3r(2 + $\sqrt{3}$)

Similarly, ∆A₁C₁E is a right angle triangle with ∠A₁C₁E = 30° and ∠C₁A₁E = 60°

∴ C₁E = $r\sqrt{3}$

∴ C₁C₂ = 2r + 2r$\sqrt{3}=2r(1+\sqrt{3})$

∴ Distance travelled by C = c = 6r(1 + $\sqrt{3}$)

∴ b - a = 3$\sqrt{3}$r and c - b = 3$\sqrt{3}$r

Hence, option (a).