A circle of radius 4cm is inscribed in ` A B C ,` which touches the side `B C a t Ddot` If `B D=6c m ,D C=8c m` then (a) the triangle is necessarily acute angled (b) `tan(A/2)=4/7` (c) perimeter of the triangle `A B C` is `42c m` (d) area of ` A B C` is `84c m^2`

D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

A circle is inscribed in a triangle A B C touching the side A B at D such that A D=5,B D=3,if/_A=60^0 then length B C equals. (a) 4 (b) (120)/(13) (c) 13 (d) 12

If A, B, C are the angles of a triangle then tan ((B+C)/2)=

Each angle A, B,C of the triangle ABC is acute and sin (B+C-A)=1 , tan (C+A-B)= sqrt(3) , find A,B and C.

A rectangle of the greatest area is inscribed in a trapezium A B C D , one of whose non-parallel sides A B is perpendicular to the base, so that one of the rectangles die lies on the larger base of the trapezium. The base of trapezium are 6cm and 10 cm and A B is 8 cm long. Then the maximum area of the rectangle is 24c m^2 (b) 48c m^2 36c m^2 (d) none of these

If A,B,C are the angles of an acute angled triangle and cos(B+C-A)=0, sin (C+A-B)=(sqrt(3))/2 , find the values of A,B , and C.

If a , b , c are the sides of triangle , then the least value of (a)/(c+a-b)+(b)/(a+b-c)+(c )/(b+c-a) is

In a triangleA B C ,/_B=90^0 and b+a=4. The area of the triangle is maximum when /_C is (a) pi/4 (b) pi/6 (c) pi/3 (d) none of these

The sides of triangle ABC satisfy the relations a + b - c= 2 and 2ab -c^(2) =4 , then the square of the area of triangle is ______