SOLUTION: A triangle with sides of length 36 cm, 77 cm, and 85 cm are inscribed in a circle. Inside the triangle a second circle is inscribed. What is the area in square centimetres, between

Notice that the given triangle is a right-angled triangle, since

    36^2 + 77^2 = 7225 = 85^2.


Since this triangle is inscribed to the larger circle, its hypotenuse is the DIAMETER of the larger circle.


Thus the larger circle's diameter is 85 cm;  hence, the larger circle's radius is R = 85/2 = 42.5 cm.


Next, the radius of the inscribed circle is (as for any right angled triangle)

    r =  =  = 14 cm

where "a" and "b" are the legs, 36 cm and 77 cm, while "c" is the hypotenuse 85 cm.


Now the area between the circles is  

     =  =  =  = 5058.745 cm^2.    ANSWER