 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says prove that the line of centers of two intersecting circles subtends equal angles at the two points of intersection. So let us see the solution to this one. Now first to fall let us write down what is given to us in the question. Now we are given two circles with centers A and B which intersect each other at the point C and D. So we have two circles with centers A and B which intersect each other E and D. Now we have to prove that the line of centers of two intersecting circles subtends equal angles at the two points of intersection. So we see that we have to show here that angle A, C, B is equal to angle A, D, B. That means we have to show that this angle is equal to this angle. Angle A, C, B equals to angle A, D, B. So first to fall we do some kind of construction here that will help us solving this question. The construction here would be we join A to C, A to D, B to D and B to C. So we join A, C, A, D, B, D and B, C. Now we can start with the proof to this question. First of all we see that in triangles A, C, B that means this triangle and triangle A, D, B that means this triangle we have A, C is equal to A, D because these are the radii of the same circle that is this center, the circle with center A. Also we have V, C is equal to B, D. Again because these are the radii of the same circle, A, B is common in both the cases. So by side, side, side criteria we have triangle A, C, B is congruent to triangle A, D, B. So let us just write down what we have seen here. We have seen that in triangles A, C, B and A, D, B we have first A, C is equal to A, D because these are the radii of same circle. Now again for the same reason we have B, C is equal to B, D and we have the side A, B as common in both the triangles. So we say that A, B is equal to A, B since that is a common site. So by side, side, side criterion of congruence we have triangle A, C, B is congruent to triangle A, D, B. This implies that angle A, C, B is equal to angle A, D, B that means this angle is equal to this angle and this we get by C, P, C, T. That means congruent part of congruent triangle or corresponding parts of congruent triangles hence proved. So I hope that you understood the question and enjoyed the session. Have a good day.