Let `D` be the middle point of the side `B C` of a triangle `A B Cdot` If the triangle `A D C` is equilateral, then `a^2: b^2: c^2` is equal to `1:4:3` (b) `4:1:3` (c) `4:3:1` (d) `3:4:1`

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

If the middle points of the sides of a triangle are (-2,3),(4,-3),a n d(4,5) , then find the centroid of the triangle.

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

In triangle A B C , if cosA+cosB+cosC=7/4, t h e n R/r is equal to 3/4 (b) 4/3 (c) 2/3 (d) 3/2

If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b : c is (a). 1:2:3 (b). 1:3:5 (c). 2:3:4 (d). 1:2:4

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 2asinC/3 (b) 2bsinC/3 (c) 2csinB/3 (d) 2csinC/3

D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

Find the length of altitude through A of the triangle A B C , where A-=(-3,0)B-=(4,-1),C-=(5,2)

Let A D be a median of the A B Cdot If A Ea n dA F are medians of the triangle A B Da n dA D C , respectively, and A D=m_1,A E=m_2,A F=m_3, then (a^2)/8 is equal to (a) m_2^2+m_3^2-2m_1^2 (b) m_1^2+m_2^2-2m_3^2 (c) m_1^2+m_3^2-2m_2^2 (d) none of these