Question

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distances from each other 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.

∠A = ${60}^{\circ }$

∠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 = 2 AM = 2 $\sqrt{300}$

= 2 × 10$\sqrt{3}$ = 20$\sqrt{3}$