In triangle ABC, medians AD and CE are drawn AD = 5, angle DAC = pi//8, and angle ACE = pi//4 , then the area of the triangle ABC is equal to

If H is the orthocentre of triangle ABC, R = circumradius and P = AH + BH + CH , then

In an acute angled triangle ABC , let AD, BE and CF be the perpendicular opposite sides of the triangle. The ratio of the product of the side lengths of the triangles DEF and ABC , is equal to

The orthocenter of the triangle formed by the lines xy=0 and x+y=1 is

Triangle ABC has vertices (0, 0) (11, 60) and (91, 0). If the line y= kx cuts the triangle into two triangles of equal area, then k is equal to :

If the perimeter of the triangle formed by feet of altitudes of the triangle ABC is equal to four times the circumradius of Delta ABC , then identify the type of Delta ABC

Orthocenter of an equilateral triangle ABC is the origin O. If vec(OA)=veca, vec(OB)=vecb, vec(OC)=vecc , then vec(AB)+2vec(BC)+3vec(CA)=

If P is a point on the altitude AD of the triangle ABC such the /_C B P=B/3, then AP is equal to

If G is the centroid of triangle ABC , prove that area triangle AGB = 1/3 area triangle ABC .

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .