 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says a circular park of radius 20 meters situated in a colony, three boys Ankush, Sayyed and David 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. Now here let a, b and c be the points where Ankush, Sayyed and David are sitting since it's given to us that they are sitting at equal distances so we have a, b is equal to b, c is equal to a, c that means a, b, c is an equilateral triangle. Now o, b being the radius of this circular park is equal to 20 meter. So let us start with the solution to this question. Let a, b, c is an equilateral triangle of site x meters clearly. We can say that b, m that is this is equal to b, c by 2, b, c is 2x so 2x by 2 is equal to x meters. Now we say that b, m is b, c by 2 because we know that if we draw a perpendicular from the center of the circle to a chord then it bisets the chord so we have b, m is equal to x meters. Now in right angle triangle a, b, m we have m square is equal to a, b square minus b, m square and this we get by Pythagoras theorem. We can write this as 2x the whole square minus x square because a, b is equal to 2x and b, m is equal to x. This is equal to 4x square minus x square that is equal to 3x square. Now a, m square is equal to 3x square so this implies that a, m is equal to root 3x because we take square root on both the sides. Now o, m can be written as a, m minus o, a so o, m is equal to a, m minus o, a. Now a, m is root 3x that we have just found out and o, a is 20 being the radius of circular path so o, m is root 3x minus 20 meter. Now in right angle triangle o, b, m that is this triangle again by the Pythagoras theorem we have o, b square is equal to o, m square plus b, m square. Now we have o, b we have is 20 so we have 20 square is equal to o, m is root 3x minus 20 so o, m square is root 3x minus 20 the whole square and b, m square will be x square. This implies 400 is equal to x square plus 3x square minus 40 root 3x plus 400. Now 400 gets cancelled from both the sides and we have 3x square plus x square is 4x square minus 40 root 3x is equal to 0. This implies now in these two terms we have 4x common so we take out 4x and in the bracket we have x minus 10 root 3 equal to 0. Since x is not equal to 0 therefore we have x minus 10 root 3 equal to 0 and this implies that x is equal to 10 root 3. Now bc is twice of bm or we can say 2x or we can say 20 root 3. Now we know that each string is of equal length so we can say that length of each string is equal to 20 root 3 meter and this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.