A circular park of radius 20m is situated in a colony Three boys Ankur, Syed and David re sitting - Maths - Circles

Question

A circular park of radius 20m is situated in a colony Three boys
Ankur, Syed and David re sitting at equal distance on its boundary
each having a toy telephone in their hand to talk each other Find
the length of the string of each phone This is a text ques (Exrcise
10 4 ques no 6) Any one plz help me to answer this!

ramandeep.singh · Accepted Answer

It is given that AS = SD = DA

Therefore, ΔASD is an equilateral triangle.

OA = r = 20 m

Medians of equilateral triangle pass through the circumcentre (O) of the equilateral triangle ASD. We also know that medians intersect each other in the ratio 2: 1. As AB is the median of equilateral triangle ASD, we can write

∴ AB = OA + OB = (20 + 10) m = 30 m

In ΔABD,

AD² = AB² + BD²

⇒AD² = (30)² + $(\frac{AD}{2})^{2}$

Therefore, the length of the string of each phone will be $20 \sqrt{3}$ m.

âˆ´ AB = OA + OB = (20 + 10) m = 30 m In Î”ABD, AD2 = AB2 + BD2 â‡’AD2 = (30)2 + $(\frac{AD}{2})^{2}$

Therefore, the length of the string of each phone will be $20 \sqrt{3}$ m