 In this theorem, we will be going through the converse of the previous theorem, right? In the previous theorem, you remember, it was given that if, you know, if two arcs of a circle or congruent circles are congruent, then the corresponding chords were equal. Now, the converse of this would be if two chords of a circle or two chords of a circle or of congruent circles are equal, then corresponding arcs are congruent. That's what we have to prove. Okay? So why are we talking about one circle and two congruent circles is the same case because you can have two equal chords within the circle itself, or you can have two chords in two different circles, but both the circles are congruent. That is, they have same radii. Okay? So now let's take this general case where we have two circles and what is given? It's given that PQ is equal to RS. Two chords are equal and you have to prove, to prove. What do we need to prove? PQ arc is length, arc rather PQ arc is congruent to RS, arc RS, okay? Congruent to arc RS. This is what we need to prove. Okay? So how to go about it? So, okay, so let's take, so let me just try it, okay? So now there are three possibilities. Either we are talking about PQ as the major arc or PQ as the minor arc, but in both the cases you will see the result is the same. So let us consider these two triangles. So let's take in triangle, triangle OPQ and triangle O dash RS, what do we have guys? OP is equal to OR, is equal to R, both are same radius circle, right? Similarly, OQ is equal to OS is equal to R and PQ is equal to RS. This was given, right? Therefore triangle OPQ is congruent to triangle O dash RS. I watched criteria guys. You know, this is SSS, congruence criteria, right? So you have studied this already, so criterion, correct? No. So then what do we now infer that angle POQ will be equal to angle R O dash S reason being corresponding parts of congruent triangle, right? So hence, if POQ is equal to R O dash, that means measure of arc PQ is equal to measure of degree measure of arc RS, okay? When degree measures are same, we know that the arcs are congruent. So PQ is congruent to RS, right? If PQ is congruent to RS, therefore QP arc will be also congruent to SR, okay? In both the cases, why? Because this is nothing but circumference minus, if you have the same radius circle, circumference minus minor arc will be equal to major arc and if minor arcs are equal, major arcs will also be equal. So what is QP and how do we differentiate PQ and QP? So when you go from P to Q like that, anticlockwise, this is PQ arc PQ and when you go from Q to P like that, so this is arc QP, this is the major arc, this is the major arc, isn't it? So both minor and major arcs are same, minor arc, okay guys? So hence, you know, both cases, both in both the cases, the arcs are congruent, okay?