Question

Three boys, Ankur, Syed and David are sitting at equal distances on the boundary of a circular park of radius $20m.$ Each of them has a toy telephone to talk to each other. Find the length of the string that connects the telephones of any two of the boys. The distance from the centre of the park to the strings is 10m.

• A. circumference
• B. chord
• C. tangent
• D. radius

Answer 1

The correct option is A

circumference

Let Ankur, Syed and David be denoted by $A,S$ and $D$ respectively in the circular park.

$OS=OD=OA=20m$ [Radius $=20m$]

Construction: Draw $OM\perp SA$

OM= 10 m

Now, $AS=SD=AD$

In $△AMO$

Applying Pythagoras Theorem

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

$=400-100=300$

$\Rightarrow AM=\sqrt{300}$

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

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