 Hello and welcome to the session. Today I will help you with the following question. The question says draw a circle and two lines parallel to a given line such that one is a tangent and the other a secant to the circle. We know that a tangent to a circle is a line that intersects the circle at only one point. So we will draw a tangent to the circle with center O. So this line AB is a tangent to a circle that intersects the circle at a point P only and also secant to a circle is a line that intersects the circle at two points. So this line CD is the secant to the circle which is intersecting the circle at the points Q and R. This is the key idea for this question. Now let's move on to the solution. First of all we will draw a circle. As you can see we have drawn a circle with center O and AB is any given line. Our basic aim is to draw two lines parallel to this given line such that one is a tangent and the other a secant to the circle. Now we shall draw a perpendicular to the line AB which passes through the center of the circle O. Consider a point P on the line AB. From P we will draw a perpendicular to this line AB which will pass through the center of the circle O. As you can see we have drawn a perpendicular through the point P passing through O. Let's mark this point Q that is this perpendicular is intersecting the circle at the point Q. At Q we will draw a line now at Q as you can see we have drawn a line CD. We know that tangent to a circle is a line that intersects the circle at one point. So the line CD would be a tangent to the circle which is intersecting the circle at the point Q. Also we know that the tangent to a circle is perpendicular to the radius through the point of contact. So this angle that is angle OQC would be 90 degrees as the tangent CD is perpendicular to the radius OQ through the point of contact Q. So we say thus angle OQC is equal to 90 degrees. Also since we had drawn the perpendicular at the point P so we have angle OPB is also 90 degrees. We know that lines are parallel if the alternate interior angles are equal. Now in this case angle OQC is 90 degrees and angle OPB is 90 degrees that is both these angles are equal and these are the alternate interior angles. So we can say that AB is parallel to CD. So we have got the tangent CD parallel to the given line AB. Next we are supposed to draw secant to the circle parallel to the given line AB. For this let's consider one point on this line PQ let this be point R. Now at R we will draw a perpendicular as you can see we have drawn a perpendicular at the point R which is intersecting the circle at two points name it E and F and we know that a secant to a circle is a line that intersects the circle at two points thus we can say that EF is the secant to the circle. Now this line EF is perpendicular at R so the angle PRE is 90 degrees and we already know that angle RPB is also 90 degrees. So the alternate interior angles that is angle RPB and angle PRE are equal thus we say that AB is parallel to EF. Thus AB is parallel to the secant EF. Finally we have got two lines parallel to the given line AB. One is a tangent to the circle that is the line CD and the other is the secant to the circle that is EF. So hope you enjoyed the session have a good day.