 Hello and how are you all today? The question says, if two chords of a circle intersect within the circle, proof that the line joining the point of intersection to the center makes equal angle with the chord or the chords. Now this is the figure that will help us in proving it. I need to prove that. First of all it's given to me that AB is equal to CD that is the equal chord without intersecting within the circle. I have named that point as P. I need to prove that the line joining the point of intersection to the center makes equal angle with the chord. Now let us quickly write down whatever is given to us in the question. We are given that the chords are equal to each other that means AB is equal to CD. I need to prove that angle. Let me first draw OE perpendicular and then OF perpendicular here. So I need to prove that angle O is equal to angle OPF and for this the construction I did was I have drawn OE perpendicular on AB, F perpendicular on CD and then also I have joined OP. Let us start with our solution. Now in triangle OEP and OFP OEP and OFP I know that angle OEP is equal to angle OFP. This is by construction each hour 90 degree. OP is the common side P is equal to O because equal chords from the center. So the distance are equal. This is equal to each other. They both are 90 degree each and this is the common side. So therefore triangle OEP is congruent to triangle OFP RHS congruency by theory. So therefore I can say that angle OPE is equal to angle OPF because chorus of the congruent triangles are equal. So by that is congruent corresponding part of congruent triangle. So this is what I needed to prove. So this completes my session. Hope you enjoy.