In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is (fig) `4:2sqrt(3)` (b) `6+4sqrt(3)` `12+(7sqrt(3))/4` (d) `3+(7sqrt(3))/4`

The area of the triangle whose sides are 6,5,sqrt(13) ( in square units ) is

An equilateral triangle S A B is inscribed in the parabola y^2=4a x having its focus at Sdot If chord A B lies towards the left of S , then the side length of this triangle is (a) 2a(2-sqrt(3)) (b) 4a(2-sqrt(3)) (c) a(2-sqrt(3)) (d) 8a(2-sqrt(3))

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

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

One angle of an isosceles triangle is 120^0 and the radius of its incircle is sqrt(3)dot Then the area of the triangle in sq. units is (a) 7+12sqrt(3) (b) 12-7sqrt(3) (c) 12+7sqrt(3) (d) 4pi

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

Plot the points (2,3), (6,3) and (4,7) in a graphsheet. Join them to make it a triangle. Find the area of the triangle.

The vector vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are sides of a triangle ABC. The length of the median through A is (A) sqrt(18) (B) sqrt(72) (C) sqrt(33) (D) sqrt(288)

A right triangle has perimeter of length 7 and hypotenuse of length 3. If theta is the larger non-right angle in the triangle, then the value of costhetae q u a ldot (sqrt(6)-sqrt(2))/4 (b) (4+sqrt(2))/6 (4-sqrt(2))/3 (d) (4-sqrt(2))/6