In `triangle ABC` internal angle bisector AI,BI and CI are produced to meet opposite sides in `A',B',C'` respectively. Prove that the maximum value of `(AIxxBIxxCI)/(A A'xxBB'xxC C')` is `8/27`

If A,B,C are the angles of a triangle, prove that the maximum value of cos A cos B cos C "is" (1)/(8)

In triangle ABC,angleC=(2pi)/3 and CD is the internal angle bisector of angleC meeting the side AB at D. If Length CD is equal to

In a DeltaABC, a,b,c are the sides of the triangle opposite to the angles A,B,C respectively. Then the value of a^3sin(B-C)+b^3 sin(C-A)+c^3 sin(A-B) is equal to

In triangle ABC if a,b,c are sides opposite of angles A, B, C respectivgely, then which of the following is correct ?

A triangle A B C is inscribed in a circle with centre at O , The lines A O ,B Oa n dC O meet the opposite sides at D , E ,a n dF , respectively. Prove that 1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/triangle

In a triangle ABC , if a,b,c are the sides opposite to angles A , B , C respectively, then the value of |{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}| is

If A,B,C are the angles of a triangle, find the maximum values of : sin A sin B sin C

If A,B,C are the angles of a triangle, find the maximum values of : sin A+ sinB+ sin C

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is