Rectangular Car...

If C is a point on the line segment joining A (-3, 4) and B(2, 1) such that AC = 2 BC, then the coordinate of C is

The point on the line 3x + 4y = 5, which is equidistant from (1, 2) and (3, 4) is

Consider, three points
P = [ - sin (β - α), - cos β],
Q = [cos (β - α), sin β]
and R = [cos (β - α + θ), sin (β - θ)]
where 0 < α, β , θ < π/4. Then,

The x - co ordinate of the incentre of the triangle that has the coordinates of mid - points of its sides as (0, 1) (1, 1) and (1, 0 ) is

The equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5 is

The circumcentre of the triangle formed by the lines y = x, y = 2x and y = 3x + 4 is

Circumcentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4) is

The circumcentre of a triangle formed by the lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0, is

If O( 0, 0 ), P( 3,4 ), Q( 6,0 ) be the vertices of the ∆OPQ.The point R inside ∆OPQ is such that the triangles OPR, PQR and OQR are of equal area. Then, the coordinates of R are

If a vertex of a triangle is (1, 1) and the mid-points of two sides through the vertex are ( -1, 2) and (3, 2), then the centroid of the triangle is