Question

Question:-

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

-Topic :- Circles
​

Answer 1

Question :-

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

Answer:-

Let Ankur, Syed and David be represented be A,S and D respectively.

Let PD = SP = SQ = QA = AR = RD = x

In ∆OPD

»» OP² = 400 - x²

=> OP = √400-x²

=> AP = 2√400-x² + √400-x²

= 3√400-x²

Now, In ∆APD,

PD² = AD² - DP²

=> x² = (2x)² - (3√400-x²)²

=> x² = 4x² - 9(400-x²)

=> x² = 4x² - 3600 + 9x²

=> 12x² = 3600

=> x² = 3600/12 = 300

=> x = 10√3

Now, SD = 2x = 2 × 10√3 = 20√3

Therefore, ASD is an equilateral triangle.

=> SD = AS = AD = 20√3

Hence, the length of string of each phone is 20 √3m.

Refer to the above

attached