 Hello and how are you all today? My name is Priyanka and let us discuss this question. It says two circles of radii 5 centimeter and 3 centimeter intersect the two points and the distance between these center is 4 centimeter. You need to find the length of the common chord. So the diagram that will help us in finding out the solution is this. Here we are given that two circles are of radii 5 centimeter and 3 centimeter and the distance between them is given to us as 4 centimeter. What we need to find out is this length of this common chord. So there is precedon with our solution. Here we are given that O A is equal to 5 centimeter. O dash A is equal to 3 centimeter and the distance between O O dash is equal to 4 centimeter. We need to find length of the common chord that is A B. So let us proceed on with our proof. Now in triangle let's say O A O dash that is this big triangle. We know the measurement of all the three sides. So we can find out the area of this triangle by using Huron's formula which says let us first find out S that is the sum of or that is the perimeter of the triangle divided by 2. The answer comes out to be 12 by 2 that is further equal to 6 centimeter. The area can be find out by using the formula S S minus A S minus B S minus C where S we have found out to be 6 and A B C are the sides of this triangle. So 6 minus 5, 6 minus 3 and 6 minus 4 that will further be 6 into 1 into 3 into 2. We can write 6 as 3 into 2. So we have 3 k 2 pairs and we have 2 k 2 pairs. Right? So we have 3 into 2 that is further equal to 6 centimeters. Now the area is found out to be 6 centimeter square. Also we know that we can find out the area of a triangle that will be O A O dash itself and we can use the formula that is half into base into altitude. Now we found out that the area of this triangle is 6. So 6 is equal to half into base of this triangle is 4 centimeters into altitude that is a n that is 6 into 2 divided by 4 equal to a m that is further equal to 3 centimeters. Now further we need to find out the length of A B. So that will be twice of a m because we can write that A B is equal to twice the length of a m because line from the center of the circle to the chord bisects the chord. Right? So this is O m is the line from the center of the circle to the chord A B. So that means it will be bisecting it. The value of a m we have got to be 3 centimeters. So m B will also be 3 centimeters that is twice. So therefore we have A B equal to 2 into 3 that is 6 centimeters length. So this is our final answer to the session. Hope you enjoyed. Have a nice day.