 In this video, we are going to prove that if from an external point P of a circle tangent segment Pt is drawn and The secant Pab is drawn secant is something that intersects the circle in two points It's basically a line. So if Pt and Pab are drawn then there is a relationship like this P a times Pb is equal to Pt square and we need to prove this How do we approach this? We approach this by proving some triangles that we see in this figure as similar first and We have constructed some chords as well So we had Pt and Pab so we joined t and a and t and b to get two chords And we will make use of alternate segment theorem to prove triangle similar But which triangles are we talking about? We are talking about triangle Pt a and Triangle Tbp. So which is triangle Tbp? It's this bigger triangle. It's this bigger triangle Let me just quickly draw the figure. So this one and the triangle Pt a is this smaller one I can draw it like this and We are going to prove that these two triangles are similar That means their sides are in equal ratios and their corresponding angles are equal first of all I have this angle Tpb or Tpa common between both of the triangles I'll just mark it here. So can I write angle Tp a to be congruent with angle Btp? Yes, remember the order of points that I took to write Tp a so I chose the middle one first Then we went to P and then to a so similar thing can be can be done here angle Btp So angle Tp a is congruent with angle Bp t and the reason for this is that this is a common angle What's the second element that I can find which will prove that the triangles are similar Another angle that I can talk about using alternate angle theorem is that if we look at the chord ta and Pt is the tangent. So the angle made here shown in orange angle atp so angle atp is going to be congruent with The angle made by the chord in the alternate arc And this is the alternate arc and the angle made by that chord in the alternate arc is this angle Pbp and reason is Alternate segment theorem now if two corresponding Angles of two triangles are congruent then the triangles are similar So can I write triangle Pt a is similar to triangle Pbt And now since these two triangles are similar their corresponding sides are in equal ratios And so therefore we can write P a divided by Pt should be equal to Pt divided by Pb And so from this relationship if we just take this ratio and cross multiply We find that P a times Pb is equal to Pt square and this is how we have shown this result to be true