 Hello and welcome to the session. In this session we discussed the following question which says find the coordinates of the circumcentre of the triangle whose vertices are 8, 6, 8 minus 2 and 2 minus 2. Also find its circum radius. So we are given the vertices of a triangle. We have to find the coordinates of the circumcentre of the triangle. We also need to find the circum radius. So let's see how we do this. Consider this triangle ABC where A has coordinates 8, 6, B has coordinates 8 minus 2 and C has coordinates 2 minus 2. Let P with coordinates XY be the circumcentre of triangle ABC. That is this is point P. It is the circumcentre for this triangle ABC. We know that circumcentre of a triangle is equidistant from the vertices of a triangle. This means that PA is equal to PB is equal to PC. Or you can also say that PA square is equal to PB square is equal to PC square. Now we know how to find the distance between two points when the coordinates are given. Consider a point A with coordinates X1, Y1 and a point B with coordinates X2, Y2. Then the distance between the two points A and B is given by AB. And this is equal to square root of X2 minus X1 whole square plus Y2 minus Y1 whole square. Or you can say that AB square is equal to X2 minus X1 whole square plus Y2 minus Y1 whole square. So using this we will find PA square PB square and PC square. We have the coordinates of point P as XY and coordinates of point A as 86. So we will find out PA square this is equal to 8 minus X whole square plus 6 minus Y whole square. Now coordinates of P is XY and coordinates of B is 8 minus 2. So now PB square is given as 8 minus X whole square plus minus 2 minus Y whole square. Or you can say PB square is equal to 8 minus X whole square plus Y plus 2 whole square. Next we will find out PC square for that we need coordinates of point P which is XY and coordinates of point C which is 2 minus 2. So PC square is equal to 2 minus X whole square plus minus 2 minus Y whole square. Which means PC square is equal to 2 minus X whole square plus Y plus 2 whole square. Now that we had PA square is equal to PB square is equal to PC square. So first we take PA square is equal to PB square. So this would mean 8 minus X whole square plus 6 minus Y whole square is equal to 8 minus X whole square plus Y plus 2 whole square. Now solving further we get 64 plus X square minus 16 X plus 36 plus Y square minus square Y is equal to 64 plus X square minus 16 X plus Y square plus 4 Y plus 4. Now X square X square cancels Y square Y square cancels minus 16 X minus 16 X cancels 64 cancels with 64. And we have 16 Y is equal to 32 which means Y is equal to 32 upon 16 which means Y is equal to 2. Next we take PB square equal to PC square which means 8 minus X whole square plus Y plus 2 whole square is equal to 2 minus X whole square plus Y plus 2 whole square. Now Y plus 2 whole square Y plus 2 whole square cancels. So on solving this we get 64 plus X square minus 16 X is equal to 4 plus X square minus 4 X. X square X square cancels so we have 12 X is equal to 16 which means X is equal to 60 upon 12. That is we have X is equal to 5. So thus we get the coordinates of the circumcentre P is 5, 2. We also had to find out the circum radius which is given as PA which is equal to PB which is equal to PC. Since PA, PB, PC are equal and this is equal to square root of 8 minus X whole square plus Y plus 2 whole square. Now we put the values of X and Y so this is equal to square root of 8 minus 5 whole square plus 2 plus 2 whole square which further gives us square root of 3 whole square plus 4 whole square. And this is equal to square root of 9 plus 16 that is equal to square root of 25 which is equal to 5. So you can say circum radius is equal to 5 units. So this completes our session. Hope you have understood the solution of this question.