In an acute triangle `A B C` , if the coordinates of orthocentre `H` are `(4,b)` , of centroid `G` are `(b ,2b-8)` , and of circumcenter `S` are `(-4,8)` , then `b` cannot be .

If in the triangle ABC , B = 45^@ , then a^4 + b^4 +c^4 =

If in a triangle ABC , a=5,b=4 ,A = (pi)/( 2) +B then C

If (1,4) is the centroid of a triangle and the coordinates of its any two vertices are (4,-8) and (-9,7), find the area of the triangle.

In each of the following vertices of a triangles are given. Find the coordinates of centroid of each triangle. (4, 7), (8, 4), (7, 11)

In triangle A B C , the equation of side B C is x-y=0. The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is

Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5,-4) . Then the coordinates of the circumcenter are (1,2)dot Statement 2 : In a right-angled triangle, the midpoint of the hypotenuse is the circumcenter of the triangle.

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a^2+1,a^2+1) and (2a ,-2a), then find the orthocentre.

Find the orthocentre of Delta A B C with vertices A(1,0),B(-2,1), and C(5,2)

In any triangle ABC, prove that a cos A+b cos B +c cos C =(8 triangle^(2))/(abc) .

In a triangle A B C prove that a//(a+c)+b//(c+a)+c//(a+b)<2