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`

Let D be the middle point of the side BC of a triangle ABC. If the triangle ADC is equilateral, then a^(2) : b^(2) : c^(2) is equal to

In triangle ABC, if sin A cos B=(1)/(4) and 3tan A=tan B, then cot ^(2)A is equal to (a)2 (b) 3 (c) 4 (d) 5 .

A B C D is a square. E is the mid-point of B C and F is the mid-point of C D . The ratio of the area of triangle A E F to the area of the square A B C D is (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 3 : 8

The mid points of the sides of a triangle A B C along with any of the vertices as the fourth point make a parallelogram of area equal to: a r\ ( A B C) (b) 1/2a r\ ( A B C) 1/3a r\ ( A B C) (d) 1/4\ a r\ ( A B C)

If a=2b, then a:b=2:1 (b) 1:2( c) 3:4 (d) 4:3

The product of the arithmetic mean of the lengths of the sides of a triangle and harmonic mean of the lengths of the altitudes of the triangle is equal to: a. 1 b. 2 c. 3 d. 4

If a,b,c are the sides of a triangle such that a:b:c=1:sqrt(3):2, then ratio A:B:C is equal to a.3:2:1b.3:1:2 c.1:2:3 d.1:3:2

The ratio of the areas of the incircle and circumcircle of an equilateral triangle is (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 1 : 9

If A-B=pi/4, then (1+tan A)(1-tan B) is equal to 2 b.1 c.0 d.3

The ratio of the area of a square of side a and that of an equilateral triangle of side a, is 2:1 (b) 2:sqrt(3)4:3( d) 4:sqrt(3)