Question

A circular park of radius 25m is situated in a Colony. Three boys Ram, Shyam and Sunder are sitting at equal distance on its boundary each having toy telephone in his hand to talk to each other. Find the length of the string of each phone

Answer 1

Length of each string $=43.30\ m$

Step-by-step explanation:

The points where Ram, Shyam and Sunder are sitting is at the point on the circle joining them will form an equilateral triangle.

So from the schematic we can observe the geometric relation.

From the $\Delta ADO$:

It is the property of an equilateral triangle that its altitude is also its median.

So,

$AD=AO.\cos30$

• Since radius is 25m and the line AO is radius as of the circle.

$AD=25\times \cos30$

$AD=21.65\ m$

Now the length of the string will be the length of the equilateral triangle.

Length of each string $=2\times AD$

Length of each string $=2\times 21.65$

Length of each string $=43.30\ m$

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TOPIC: circumcircle

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