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 (a) 3b^2=a^2-c (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_2, 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 in A B C ,A C is double of A B , then the value of cot(A/2)cot((B-C)/2) is equal to 1/3 (b) -1/3 (c) 3 (d) 1/2

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to (a) a+b (b) b+c (c) c+a (d) a+b+c

IF the lengths of the side of triangle are 3,5A N D7, then the largest angle of the triangle is pi/2 (b) (5pi)/6 (c) (2pi)/3 (d) (3pi)/4

Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixed points on the parabola. Let C be a moving point on the parabola between Aa n dB such that the area of the triangle A B C is maximum. Then the coordinates of C are (a) (1/4,1) (b) (4,4) (c) (3,2/(sqrt(3))) (d) (3,-2sqrt(3))

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