The incentre of the triangle with vertices $$\left( {1,\,\sqrt 3 } \right),\left( {0,\,0} \right)$$ and $$\left( {2,\,0} \right)$$ is

Lt $$PQR$$ be a right angled isosceles triangle, right angled at $$P(2, 1)$$. If the equation of the line $$QR$$ is $$2x + y = 3,$$ then the equation representing the pair of lines $$PQ$$ and $$PR$$ is

If $${x_1},\,{x_2},\,{x_3}$$ as well as $${y_1},\,{y_2},\,{y_3}$$, are in G.P. with the same common ratio, then the points $$\left( {{x_1},\,{y_1}} \right),\left( {{x_2},\,{y_2}} \right)$$ and $$\left( {{x_3},\,{y_3}} \right).$$

If $$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \right)} \right)$$ and $$S\left( {a,b} \right)$$ are the vertices of a parrallelogram $$PQRS,$$ then