 Hello and welcome to the session my name is Mansi and I am going to help you with the following question. The question says 3 girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 meter drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 meter each, what is the distance between Reshma and Mandip? So what we need to find out in this question is the distance between Reshma and Mandip. Now let us see the interpretation of this question. Let R be the point where Reshma is standing, S be the point where Salma is standing and M be the point where Mandip is standing. So as per given in the question we see OR is the radius of the circle that is 5 meter, R between R and S the distance is 6 meter and so is the distance between Salma and Mandip that is also 6 meter. Now what we have to find out in this question is RM that means we have to find out the distance between Reshma and Mandip. So let us start with the solution to this question. Since we have to find RM so for that first of all we have to find KR. So let KR be equal to X meter. Now we have to find out KR first of all because the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle therefore we can say that here KS is the internal angle bisector of angle RSM so KS divides RM in the ratio 6 is to 6 that is equal to 1 is to 1 or we can say that K is the midpoint of RM. So what we can do now is we can find out the value of KR and then we multiply it by 2 to get the value of RM. Again we see here that KS is the internal angle bisector of angle RSM so it divides the opposite sides that meet RK and KM in the ratio of RS is to SM that is 6 is to 6 that is 1 is to 1 so RK should be equal to KM so we simply find out the value of RK and then we multiply it by 2 to get the value of RM. So now let us see how we find out the value of RK first of all let us consider the triangle ORS so we draw it separately first of all this is the triangle ORS OR is 5 meter being the radius of the circle RS is the distance between Reshma and Salma that is 6 meter so now from here we see that we have to find out RK we see that since OR and OS both of them they are the radius of this circle so both of them will be equal since OR is 5 meter so OS will also be 5 meter now we see that area of triangle ORS is equal to half of X into 5 that means this is X this we've considered in the first part of the question we see that area of a triangle is half base into height base here is 5 meter and height is RK that is X meter so this we get because area is equal to half into base into height also we see that area of triangle ORS can also be written as half RS into now we drop a pentacular from O to the line RS we name it OL so area is half RS that is base into height and height is OL now we see that area of triangle ORS will be same therefore half into X into 5 is equal to half into RS into OL now we see that we have the value of RS with us as 6 meter now we have to find out the value of OL in order to find out X so now here we see that since we see OL is a perpendicular that we draw from the center to a chord RS so OL this bisects RS so that means RL will be equal to LS is equal to 3 meter so again we have another triangle formed here the triangle is OLR this is 90 degree let us make it more clear the triangle we have now is OLR this is 90 degree this is 5 meter this is 3 meter we have to find out the value of OL since we see that this is a right angle triangle therefore we can say that OL square is equal to OR square minus RL square OR is given to us as a radius of the circle so this is 5 square that is 25 minus RL square will be 3 square that is 9 and that is equal to 16 therefore OL will be under the root 16 and that is equal to 4 so we have the value of OL as 4 meters so now we can simply put in the values and we have X is equal to half into RS we have 6 OL we just find out 4 into 2 into 1 by 5 now here we see that we have to solve this to get the value of X so we see that this is equal to 2 in the numerator gets cancelled with 2 in the denominator we have 64 R24 by 5 and that is equal to 4.8 meter so now we have X or RK is 4.8 meter we have to find out RM so we multiply this by 2 because K is the midpoint of RM so we can say that therefore RM is equal to 2 into 4.8 meter and that is equal to 9.6 meter and this becomes our answer to this question I hope that you understood the question and enjoyed the session have a good day