 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. Now the question says, the lengths of two parallel cords of a circle are 6 cm and 8 cm. If the smaller cord is at distance 4 cm from the center, what is the distance of the other cord from the center? Now this is the circle such that a b and c d are two parallel cords. Let us start with the solution to this question. We have a b is equal to 6 cm and c d is equal to 8 cm. Let the radius of the circle be r cm. Now we draw o p perpendicular to a b and o q perpendicular to c d. Since a b is parallel to c d and o p stands perpendicular on a b, o q stands perpendicular on c d. Therefore the points o q and p are co-linear. Clearly o p is equal to 4 cm because it is given to us in the question that the smaller cord that is a b is at a distance 4 cm from the center. So we have o p is equal to 4 cm and p q are mid points of a b and c d respectively. This happens because we know that if a line is drawn from the center of a circle to a cord such that that line is perpendicular to the cord then it bisects the cord. So therefore we can say that a p is equal to b p and c q equals to q d. Therefore a p is equal to p b is equal to half of a b that is 3 cm and c q is equal to q d is equal to half of c d that is 4 cm. We see that in right angle triangle o ap that means this triangle we have o a square is equal to o p square plus a p square. This we get by Pythagoras theorem. Now we substitute in the values that we have. Now we know that o a is equal to r that is the radius of the circle. So r square is equal to o p is 4 so p square is 4 square and ap we have just found out is 3. So r square is equal to 4 square plus 3 square that is equal to 16 plus 9 that is equal to 25. So we have r square is 25 but we need just the value of r so we take square root on both the sides and we have r is equal to under the root 25 and that is equal to plus minus 5. Now we know that radius cannot be negative so we neglect the negative sign and we have r is equal to 5. Now in right angle triangle o c q that means this circle we have o c square is equal to o q square plus c q square again by the Pythagoras theorem. So r square is equal to o q square plus 4 square we just found out that r was 5. So we will have 25 is equal to o q square plus 16 this implies that o q square is equal to 9 and this implies that o q is equal to 3 hence the distance of chord c d from the center is 3 centimeter. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.