AD, BE and CF are the medians of triangle ABC whose centroid is G. If the points A, F, G and E are concyclic, then prove that `2a^(2) = b^(2) + c^(2)`

A A_1, B B_1a n dC C_1 are the medians of triangle A B C whose centroid is Gdot If points A ,C_1, Ga n dB_1 are concyclic, then

If AD,BE and CF are the altitudes of a triangle ABC whose vertex A is the point (-4,5) . The coordinates of the points E and F are (4,1) and (-1,-4) respectively, then equation of BC is

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

AD, BE and CF asre the medians of a triangle ASBC intersectiing in G. Show that /_\AGB=/_\BGC=/_\CGA=1/3/_\ABC .

AD is a median of triangle ABC. Prove that : AB+BC+AC gt 2AD

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(B L^2+C M^2)=5B C^2

If BM and CN are the perpendiculars drawn on the sides AC and BC of the Delta ABC , prove that the points B, C, M and N are concyclic.

Find the orthocentre of the triangle ABC whose angular points are A(1,2),B(2,3) and C(4,3)

A(3,2)a n dB(-2,1) are two vertices of a triangle ABC whose centroid G has the coordinates (5/3,-1/3)dot Find the coordinates of the third vertex C of the triangle.

The medians AD and BE of the triangle with vertices A(0,b),B(0,0) and C(a,0) are mutually perpendicular. Prove that a^2=2b^2 .