 Hi and welcome to the session. Let us discuss the following question. Question says fill in the blanks. Third part is a circle can have dash parallel tangents at the most. Let us now start with the solution. We know the tangent at any point of the circle is perpendicular to the radius through the point of contact. Now let us draw a circle which center row and a b and c d are two tangents to a circle. p q is the diameter of the circle, c d touches circle at point p and a b touches circle at point q. Now we know tangent at any point of a circle is perpendicular to the radius through the point of contact. Now o q is the radius a b is the tangent and q is the point of contact here. So we get o q is perpendicular to a b. Similarly we get o p is perpendicular to c d, o p is the radius, c d is the tangent and p is the point of contact here. So o p is perpendicular to c d. So we can write o q is perpendicular to a b and o p is perpendicular to c d. Now we know angle o q a is equal to 90 degrees or we can say angle p q a is equal to 90 degrees. Now angle p q a is equal to 90 degrees implies a b is perpendicular to p q. Similarly we can write c d is perpendicular to p q since angle c p q is equal to 90 degrees. These two lines are perpendicular to same line that is p q. So we get a b is parallel to c d from this discussion. We get a circle can have two parallel tangents at the most. We know tangents can be parallel only when they are perpendicular to the same line. Now two radius can be drawn in the same line only when we draw diameter of the circle. So many diameters of the circle can be drawn this way since touching the end points of the diameter will be parallel to each other. So we can write a circle can have parallel tangents at the most. So we can fill in this blank too. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.