 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says two congruent circles intersect each other at points A and B. Through A any line segment P A Q is drawn so that P Q lie on the two circles prove that B P is equal to B Q. So we have to show that B P is equal to B Q. Let us start with a solution to this question. First of all let O and O dash be the center of congruent circles. We see that A B is a common chord of these circles, common chord. Therefore arc ACB is equal to arc ADB arc ACB is equal to arc ADB. Now this implies that angle B P A that means this angle is equal to angle B Q A that means this angle this implies that angle V P A is equal to angle V Q A and this implies that V P is equal to V Q. We see that if this arc is equal to this arc then the angle that this arc subtends will be equal to the angle that this arc subtends and since angle B P A is equal to angle V Q A so B P will be equal to V Q because if we consider this as a triangle then V P and V Q are two sides opposite to these two angles. Since these two angles are equal therefore sides opposite to them will also be equal so we have V P equal to V Q hence proved. So I hope that you understood the question and enjoyed the session. Have a good day.