If the vertices of a triangle are `(sqrt(5,)0)` , (`sqrt(3),sqrt(2))` , and `(2,1)` , then the orthocentre of the triangle is `(sqrt(5),0)` (b) `(0,0)` (c)`(sqrt(5)+sqrt(3)+2,sqrt(2)+1)` (d) none of these

The incentre of the triangle with vertices (1, sqrt3 ) (0,0) (2,0) is

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

The incentre of a triangle with vertices (7, 1),(-1, 5) and (3+2sqrt(3),3+4sqrt(3)) is

The vertices of a triangle are (0,0), (x ,cosx), and (sin^3x ,0),w h e r e0ltxltpi/2 the maximum area for such a triangle in sq. units is (a) (3sqrt(3))/(32) (b) (sqrt(3)/32) (c) 4/32 (d) (6sqrt(3)) /(32)

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

Prove that (sqrt(2),sqrt(2)) (-sqrt(2), -sqrt(2) ) and (-sqrt(6 ) , sqrt(6)) are ther vertices of an equilateral triangle.

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle C is

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle C is

Prove that the points (0,0) (3, sqrt(3)) and (3, -sqrt(3)) are the vertices of an equilateral triangle.

The sum up to n terms of the series 1/(sqrt(1) + sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) +… is: