In ` A B C ,if a=10 and bcotB+ c cotC=2(r+R)` then the maximum area of ` A B C` will be (a) 50 (b) `sqrt(50)` (c) 25 (d) 5

In triangle A B C , if cotA *cotC=1/2a n dcot B* cotC=1/(18), then the value of tanC is

A circle passes through the points A(1,0) and B(5,0), and touches the y-axis at C(0,h)dot . If /_A C B is maximum, then (a) h=3sqrt(5) (b) h=2sqrt(5) (c) h=sqrt(5) (d) h=2sqrt(10)

Let A B C D be a tetrahedron such that the edges A B ,A C and A D are mutually perpendicular. Let the area of triangles A B C ,A C D and A D B be 3, 4 and 5sq . units , respectively. Then the area of triangle B C D is a. 5sqrt(2) b. 5 c. (sqrt(5))/2 d. 5/2

In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of 3 (b) 6 (c) 9 (d) none of these

If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)_d a+(log)_b d+(log)_a c+(log)_c b is (a) 4 (b) 2 (c) 1 (d)none of these

In triangle A B C ,l e tR=c i r c u m r a d i u s ,r= i n r a d i u sdot If r is the distance between the circumcenter and the incenter, the ratio R/r is equal to (a) sqrt(2)-1 (b) sqrt(3)-1 (c) sqrt(2)+1 (d) sqrt(3)+1

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

The area of triangle A B C is 20c m^2dot The coordinates of vertex A are (-5,0) and those of B are (3,0)dot The vertex C lies on the line x-y=2 . The coordinates of C are (a) (5,3) (b) (-3,-5) (-5,-7) (d) (7,5)

If a : b = c : d , then prove that (a + c) : (b + d) = sqrt(a^(2) - c^(2)) : sqrt(b^(2) - d^(2))

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c