A right triangle is drawn in a semicircle of radius `1/2` with one of its legs along the diameter. If the maximum area of the triangle is `M` , then the value of `32sqrt(3)M c` is______

If circumradius of triangle is 2, then the maximum value of (abc)/(a+b+c) is

The area of a right triangle is 6864 sq. units. If the ratio of its legs is 143 : 24 , then the value of r is ______

The triangle of maximum area with constant perimeter 12m

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

The maximum area of the triangle whose sides a,b and c satisfy 0leqaleq1,1leqbleq2 and 2leqcleq3 is

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

Let aa n db represent the lengths of a right triangles legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, the d+D equals. (a) a+b (b) 2(a+b) (c) 1/2(a+b) (d) sqrt(a^2+b^2)

Two medians drawn from the acute angles of a right angled triangle intersect at an angle pi/6. If the length of the hypotenuse of the triangle is 3 units, then the area of the triangle (in sq. units) is (a) sqrt3 (b) 3 (c) sqrt2 (d) 9