 Hello and welcome to the session. In this session we discussed the following question which says if O is the point in the exterior of triangle PQR, show that 2 times OP plus OQ plus OR is greater than PQ plus QR plus RP. First let's recall a very important fact which we will use in this question which says that the sum of any two sides of a triangle is greater than the third side. This is the key idea to be used in this question. Now we move on to the solution. Consider this triangle PQR and this O is a point in the exterior of triangle PQR and we need to show that 2 times OP plus OQ plus OR is greater than PQ plus QR plus RP. So first of all we shall join OP, OQ and OR. So now as you can see we have joined OP, OQ and OR. So first consider the triangle POQ. Now since we know that the sum of any two sides of a triangle is greater than the third side. So for triangle POQ, OP plus OQ would be greater than its third side that is PQ. Let this be equation 1. Now next consider the triangle QOR. In this again we will use the result which says that the sum of any two sides of a triangle is greater than the third side. So using this result we would get that in triangle QOR, OQ plus OR is greater than the third side of triangle QOR which is QR. Let this be equation 2. Now we consider the triangle POR. In this also we will use the same result that the sum of any two sides of a triangle is greater than the third side. So for this triangle OP plus OR is greater than the third side which is PR. Let this be equation 3. Now adding equations 1, 2 and 3 we get OP plus OQ plus OQ plus OR plus OP plus OR is greater than PQ plus QR plus PR that is 2 times OP plus OQ plus OR is greater than PQ plus QR plus RP or PR. And we were supposed to prove this. So hence proved with this we complete this session. Hope you have understood the solution for this question.