 Hello and welcome to the session. In this session, we discuss the following question which says in the given figure, OD is perpendicular to the chord AB of a circle with center O. If BC is a diameter, show that AC parallel to OD and AC is equal to 2 times OD. Before we move on to the solution, let's recall the midpoint theorem according to which we have that the line segment joining the midpoints of any two sides to the third side and is half of it. Now we have another result which says that the perpendicular from the center of a circle to the chord bisects the chord. This is the key idea for this question. Now we move on to the solution. First let's see what all is given to us in the question. This is the figure given to us. We have that AB is the chord of the circle which has the center as O. Then we are also given that BC is the diameter of the circle and OD is given to be perpendicular to the chord AB. We need to prove that AC is parallel to OD and AC is equal to 2 multiplied by OD. Now since we are given that OD is the perpendicular from the center O of the circle to the chord AB of the circle. So this means that OD bisects the chord AB since we know that the perpendicular from the center of a circle to the chord bisects the chord. So this means that the point D is the midpoint of the chord AB. Now next we are given that BC is the diameter of the circle and O is the center of the circle. So this means that O is the midpoint of BC. Now we consider the triangle ABC in this we have that D is the midpoint side AB of triangle ABC and O is the midpoint of side BC of triangle ABC. So by the midpoint theorem which we have stated in the key idea we have that the line segment joining the midpoints of two sides of triangle ABC that is the line segment OD would be parallel to the third side of the triangle ABC which is AC and OD will be equal to half of the third side of triangle ABC which is AC. That is we have now got AC parallel to OD and AC is equal to 2 multiplied by OD and we were supposed to prove this so hence proved this complete C session hope you have understood the solution for this question.