Question

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hand to talk to each other. Find the length of the string of each phone.

• A. 20√3
• B. 40√3
• C. 30√3
• D. 10√3

Answer 1

The correct option is A

20√3

Let situation of Ankur, Syed and David be A, S and D respectively in the circular path.

OS = OD = OA = 20m

construction: Draw OM $\perp$ SA

Now, AS = SD = AD

So, ASD is an equilateral triangle.

$\angle A={60}^{\circ }$

$\angle MAO={30}^{\circ }$

$MO=\frac{AO}{2}$

[In right angled triangle, the side opposite to ${30}^{\circ }$ is half of hypotenuse]

$MO=\frac{20}{2}=10$

${AM}^2={AO}^2-{MO}^2={20}^2-{10}^2$

400 - 100 = 300

$AM=\sqrt{300}$

$AS=2AM=2\sqrt{300}$

$=2\times 10\sqrt{3}=20\sqrt{3}$