 Hello and welcome to this session. In this session, we discuss the following question that says, two circles touch each other internally at point P, QPR is the tensioned at P, segments PAB and PCB meet circles at A, B, C and D. As shown in the figure, this is the figure. Show that chord A, C is parallel to chord BD. Let us first discuss the alternate segment property. According to this we have this a straight line, so the point of contact of chord is drawn the angles between are respectively equal to the angles in the alternate segment that we use for this question. Let us proceed with the solution now. This is the figure in which we have that the two circles touch each other internally when we are also given that QPR to point P, we have segment PAB meets the two circles at the points A and B and the segment PCD meet the two circles at the points C and D. And we are supposed to prove that AC is parallel to the point of contact that is this point. And from the alternate segment property we have that if a straight line touches the circle and from the point of contact a chord is drawn when the angles between the tension and the chord are respectively equal to the angles in the alternate segment. So since this is the tension and this is the chord, so the angle between the tension and the chord that is this angle would be equal to the angle in the alternate segment that is this angle. This is equal to angle that this will result one and this is using the bigger circle. So the bigger circle is the tension to the circle from the point of contact angle between the tension and the chord PB that is this angle would be equal to that is angle QPB would be equal to the angle in the alternate segment which is angle PBB. Now this will result two using the QPA and angle QPB are same these two angles are same therefore one and two we have PBB is equal to angle QPB. And from the figure we observe that these two angles are the corresponding angles and transversal such that the corresponding angles equal the parallel. Now as these two angles are the corresponding angles and they are equal therefore we see this parallel to PBB. This is what we were supposed to prove hence correct. To help you understand the solution of this question.