A circular path of radius 40m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone
Answers
Radius = OA = 40 cm (Given)
AB = BC = CA
Thus, ABC is an equilateral triangle
Medians of an equilateral triangle pass through the circumference (O) of the equilateral triangle ABC and the median intersects each other at 2: 1.
OA/OD = 2
40/OD = 2
OD = 20m
Therefore,
AD = OA + OD = 40 + 20 = 60m
In ΔADC
Using pythagoras theorem -
AC² = AD² + DC²
AC² = 60² + (AC/2)²
AC² = 3600 + AC²/4
3/4AC² = 3600
AC² = 4800
AC = 40√3
Thus, the length of the string of each phone will be 40√3.
length of the string of each phone = 40√3 m
Step-by-step explanation:
Ankur, Amit and Anand are sitting at equal distance
=> Equilateral Triangle
Let say ABC is triangle
and O is center
then AO = BO = CO = Radius = 40 m
as Triangle is equilateral
Hence ∠AOB = ∠BOC = ∠COA = 360°/3 = 120°
AB² = AO² + BO² - 2AO. BO Cos∠AOB
=> AB² = 40² + 40² - 2* 40 * 40 Cos120
=> AB² = 3200 - 3200(-0.5)
=> AB² = 3200 + 1600
=> AB² = 4800
=> AB² = 40√3
length of the string of each phone = 40√3 m
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