The triangle with vertices `(a, b), (a,a), (b,a)` is

The area of the triangle with vertices (a, b),(ar, bs), (ar^(2), bs^(2)) is

The length of the diameter of the circum circle of the triangle with vertices (a,0),(a,b) and (0,b) is

The length of the diameter of the circumcircle of the triangle with vertices (a,0) , (a,b) and (0,b) is

The area of a triangle with vertices (a,b+c), (b,c+a) and (c,a+b) is

The area of a triangle with vertices (a,b+c), (b,c+a) and (c,a+b) is

If a+b+c=lambda, then circumcentre of the triangle with vertices (a,b,c);(b,c,a) and (c,a,b) is

If the medians from A and B of the triangle with vertices A(0, b), B(0,0) and C(a, 0) are mutually perpendicular then show that a=+- sqrt2 b

Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, e), (2, b) and (a, b) be ((10)/(3), 7/3) . If alpha, beta are the roots of the equation ax^2 + bx + 1 = 0 , then the value of alpha^2 + beta^2 - alpha beta is :