If the incircle of the triangle ABC touches its sides respectively at L , M , N and if x , y , z be the circumradii of the triangles MIN , NIL , LIMwhere I is the incentre then the product xyz is equal to

Note that since angle ILB = angle INB = 90⁰, INBC is a cyclic quadrilateral, which is also the circumcircle of Tr INC. This circle has IB as its diameter. From IBC we have angle IBC = B/2 and BC = (s-b) and hence radius of the circumcircle of Tr INC is .

 

Hence the product of the radii is 

 

Using  etc.,

 

this product becomes