 Hello and welcome to the session. In this session we discussed the following question which says, in the given figure, that is this figure, O is the center if O A is equal to 5 centimeters, B X equal to 4 centimeters and O X equal to 3 centimeters, find X C. Before we move on to the solution, let's discuss one result which says that a straight line drawn from the center of a circle perpendicular to a chord sets the chord. This is the key idea that we use for this question. Let's proceed with the solution now. This is the figure given to us in which we have that O, if the center of the circle we join O A and O B also. We have joined O A, O X and O B. Now in the question we are given that O A is equal to 5 centimeters, B X is equal to 4 centimeters and O X is equal to 3 centimeters and we are supposed to find the length of X C. We suppose that the radius of the circle, this means that O A would be equal to O B would be equal to R, so they are the radii of the circle. We consider P and B C are drawn through, we draw O M perpendicular to B C. We have this O M perpendicular to the chord B C. From the key idea we know that a straight line drawn from the center of a circle perpendicular to a chord bisects the chord since perpendicular to the chord B C therefore we say that B N would be equal to N C. Next we consider the product of the segments of the chord B C which would be B X into C X. Now this could be further written as from the figure we find that B X is given by B N minus N X. So B N minus N X is B X this whole into C X which is this means that B X into C X is equal to B N minus N X this whole into C N plus N X. Now we know that C N is equal to B N, C N that is N C is equal to B N. So we can write here B N plus now using the identity we get that B X into C X is equal to B N square minus N X square B X into C X is equal to B N square minus now from the triangle N X we have is equal to O N square plus N X square by the Pythagoras theorem. So from here we have N X square is equal to O X square minus O N square. So we can write here square minus O N square B. This gives us B X into C X is equal to B N square minus O X square plus O N square or you can say that B X into C X is equal to B N square plus O N square minus now when you consider the triangle B square is equal to O N square plus N V square again by the Pythagoras theorem. So this means that B X into C X is equal to B square X square. Now we know that O V is the radius of the circle which is R. So we have B X into C X is equal to R square minus we know that R is the radius of the circle and this is equal to O V and O A. Since O A is equal to 5 centimeters so this means O V is also 5 centimeters and R is also 5 centimeters and we are also given the values of B X and O X. So we can substitute these values. So this gives us first centimeter that is B X into C X is equal to R square which would be 5 centimeter the whole square minus O X which is 3 centimeters the whole square. So this gives us 4 centimeters into C X is equal to 25 centimeters square minus 9 centimeters square or you can say that 4 centimeters into C X is equal to 16 centimeters square and here we get C X is equal to 16 upon 4 centimeters. Now 4 times is 16 so therefore we get C X is equal to 4 centimeters or finally you can say that X C is equal to 4 centimeters. So this is our final answer. This completes the session. Hope you have understood the solution of this question.